TS_PCA.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from scipy import stats\n",
    "\n",
    "import plotly\n",
    "import plotly.express as px\n",
    "\n",
    "pd.options.mode.chained_assignment = None  # default='warn'\n",
    "from IPython.core.interactiveshell import InteractiveShell\n",
    "InteractiveShell.ast_node_interactivity = \"all\"\n",
    "\n",
    "pd. options. plotting. backend = \"plotly\"\n",
    "\n",
    "import plotly.io as pio\n",
    "pio.renderers.default = 'jupyterlab'\n",
    "\n",
    "pd.set_option('precision',4)\n",
    "\n",
    "import statsmodels.api as sm\n",
    "import statsmodels.formula.api as smf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Term structure data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# TNC (Treasury Nominal Coupon) month-end spot rate files are provided as 5-year chunks of data\n",
    "# First column is 'Maturity', with rows at 0.5 year intervals, upto 100 years.\n",
    "# Other columns are for each month-end for 5 years.\n",
    "\n",
    "def ProcessInput(df,start,end):\n",
    "    l=[]\n",
    "    for year in range(start,end+1):\n",
    "        l = l+12*[str(year)]\n",
    "    NewNames = df.columns[1:].str.slice(stop=3)+pd.Series(l)\n",
    "    NewNames = (pd.Series('Maturity').append(NewNames)).reset_index(drop=True)\n",
    "    df = df.rename(columns=dict(zip(df.columns.values,NewNames)))\n",
    "    df = df.melt(id_vars='Maturity',var_name='Date',value_name='SpotRate')\n",
    "    df[\"Date\"] = (pd.to_datetime(df[\"Date\"],format=\"%b%Y\")).dt.date+pd.offsets.MonthEnd(0)\n",
    "    df[\"SpotRate\"] = df[\"SpotRate\"]/100\n",
    "    return(df)\n",
    "\n",
    "# Read in each file and process it. End result is a composite long form dataframe\n",
    "\n",
    "suffixes = ['03_07','08_12','13_17','18_22']\n",
    "dflist=[]\n",
    "for x in suffixes:\n",
    "    file = \"tnceom_\"+x+\".csv\"\n",
    "    filedf = pd.read_csv(file,skiprows=4)\n",
    "    filedf = filedf.drop(columns=filedf.columns[1],index=filedf.index[0])   # blank column and row\n",
    "    start = int('20'+x[0:2])\n",
    "    end = int('20'+x[3:])\n",
    "    dflist.append(ProcessInput(filedf,start,end))\n",
    "\n",
    "tncdf = pd.concat(dflist).reset_index(drop=True).dropna(subset=[\"SpotRate\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "TSPoints = np.array([0.5,1.0,2.0,3.0,5.0,10.0,20.0,30.0])\n",
    "TSdf = tncdf.loc[tncdf[\"Maturity\"].isin(TSPoints),:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/vnd.plotly.v1+json": {
       "config": {
        "plotlyServerURL": "https://plot.ly"
       },
       "data": [
        {
         "hovertemplate": "Date=2020-01-31<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-01-31",
         "line": {
          "color": "#636efa",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-01-31",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.0163,
          0.0151,
          0.0134,
          0.013000000000000001,
          0.013600000000000001,
          0.015,
          0.0197,
          0.0217
         ],
         "yaxis": "y"
        },
        {
         "hovertemplate": "Date=2020-02-29<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-02-29",
         "line": {
          "color": "#EF553B",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-02-29",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.0123,
          0.0109,
          0.0091,
          0.0087,
          0.0095,
          0.011200000000000002,
          0.016,
          0.0183
         ],
         "yaxis": "y"
        },
        {
         "hovertemplate": "Date=2020-03-31<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-03-31",
         "line": {
          "color": "#00cc96",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-03-31",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.0011,
          0.0013,
          0.002,
          0.0028000000000000004,
          0.0043,
          0.006999999999999999,
          0.0121,
          0.0152
         ],
         "yaxis": "y"
        },
        {
         "hovertemplate": "Date=2020-04-30<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-04-30",
         "line": {
          "color": "#ab63fa",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-04-30",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.002,
          0.0018,
          0.0018,
          0.0024,
          0.004,
          0.0059,
          0.011899999999999999,
          0.0146
         ],
         "yaxis": "y"
        },
        {
         "hovertemplate": "Date=2020-05-31<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-05-31",
         "line": {
          "color": "#FFA15A",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-05-31",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.0022,
          0.0018,
          0.0016,
          0.002,
          0.0034999999999999996,
          0.0062,
          0.0128,
          0.0161
         ],
         "yaxis": "y"
        },
        {
         "hovertemplate": "Date=2020-06-30<br>Maturity=%{x}<br>SpotRate=%{y}<extra></extra>",
         "legendgroup": "2020-06-30",
         "line": {
          "color": "#19d3f3",
          "dash": "solid"
         },
         "mode": "lines+markers",
         "name": "2020-06-30",
         "orientation": "v",
         "showlegend": true,
         "type": "scatter",
         "x": [
          0.5,
          1,
          2,
          3,
          5,
          10,
          20,
          30
         ],
         "xaxis": "x",
         "y": [
          0.0021,
          0.0018,
          0.0015,
          0.0019,
          0.0033,
          0.0064,
          0.0127,
          0.016
         ],
         "yaxis": "y"
        }
       ],
       "layout": {
        "autosize": true,
        "legend": {
         "title": {
          "text": "Date"
         },
         "tracegroupgap": 0
        },
        "template": {
         "data": {
          "bar": [
           {
            "error_x": {
             "color": "#2a3f5f"
            },
            "error_y": {
             "color": "#2a3f5f"
            },
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "bar"
           }
          ],
          "barpolar": [
           {
            "marker": {
             "line": {
              "color": "#E5ECF6",
              "width": 0.5
             }
            },
            "type": "barpolar"
           }
          ],
          "carpet": [
           {
            "aaxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "baxis": {
             "endlinecolor": "#2a3f5f",
             "gridcolor": "white",
             "linecolor": "white",
             "minorgridcolor": "white",
             "startlinecolor": "#2a3f5f"
            },
            "type": "carpet"
           }
          ],
          "choropleth": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "choropleth"
           }
          ],
          "contour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "contour"
           }
          ],
          "contourcarpet": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "contourcarpet"
           }
          ],
          "heatmap": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmap"
           }
          ],
          "heatmapgl": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "heatmapgl"
           }
          ],
          "histogram": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "histogram"
           }
          ],
          "histogram2d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2d"
           }
          ],
          "histogram2dcontour": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "histogram2dcontour"
           }
          ],
          "mesh3d": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "type": "mesh3d"
           }
          ],
          "parcoords": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "parcoords"
           }
          ],
          "pie": [
           {
            "automargin": true,
            "type": "pie"
           }
          ],
          "scatter": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter"
           }
          ],
          "scatter3d": [
           {
            "line": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatter3d"
           }
          ],
          "scattercarpet": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattercarpet"
           }
          ],
          "scattergeo": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergeo"
           }
          ],
          "scattergl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattergl"
           }
          ],
          "scattermapbox": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scattermapbox"
           }
          ],
          "scatterpolar": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolar"
           }
          ],
          "scatterpolargl": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterpolargl"
           }
          ],
          "scatterternary": [
           {
            "marker": {
             "colorbar": {
              "outlinewidth": 0,
              "ticks": ""
             }
            },
            "type": "scatterternary"
           }
          ],
          "surface": [
           {
            "colorbar": {
             "outlinewidth": 0,
             "ticks": ""
            },
            "colorscale": [
             [
              0,
              "#0d0887"
             ],
             [
              0.1111111111111111,
              "#46039f"
             ],
             [
              0.2222222222222222,
              "#7201a8"
             ],
             [
              0.3333333333333333,
              "#9c179e"
             ],
             [
              0.4444444444444444,
              "#bd3786"
             ],
             [
              0.5555555555555556,
              "#d8576b"
             ],
             [
              0.6666666666666666,
              "#ed7953"
             ],
             [
              0.7777777777777778,
              "#fb9f3a"
             ],
             [
              0.8888888888888888,
              "#fdca26"
             ],
             [
              1,
              "#f0f921"
             ]
            ],
            "type": "surface"
           }
          ],
          "table": [
           {
            "cells": {
             "fill": {
              "color": "#EBF0F8"
             },
             "line": {
              "color": "white"
             }
            },
            "header": {
             "fill": {
              "color": "#C8D4E3"
             },
             "line": {
              "color": "white"
             }
            },
            "type": "table"
           }
          ]
         },
         "layout": {
          "annotationdefaults": {
           "arrowcolor": "#2a3f5f",
           "arrowhead": 0,
           "arrowwidth": 1
          },
          "coloraxis": {
           "colorbar": {
            "outlinewidth": 0,
            "ticks": ""
           }
          },
          "colorscale": {
           "diverging": [
            [
             0,
             "#8e0152"
            ],
            [
             0.1,
             "#c51b7d"
            ],
            [
             0.2,
             "#de77ae"
            ],
            [
             0.3,
             "#f1b6da"
            ],
            [
             0.4,
             "#fde0ef"
            ],
            [
             0.5,
             "#f7f7f7"
            ],
            [
             0.6,
             "#e6f5d0"
            ],
            [
             0.7,
             "#b8e186"
            ],
            [
             0.8,
             "#7fbc41"
            ],
            [
             0.9,
             "#4d9221"
            ],
            [
             1,
             "#276419"
            ]
           ],
           "sequential": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ],
           "sequentialminus": [
            [
             0,
             "#0d0887"
            ],
            [
             0.1111111111111111,
             "#46039f"
            ],
            [
             0.2222222222222222,
             "#7201a8"
            ],
            [
             0.3333333333333333,
             "#9c179e"
            ],
            [
             0.4444444444444444,
             "#bd3786"
            ],
            [
             0.5555555555555556,
             "#d8576b"
            ],
            [
             0.6666666666666666,
             "#ed7953"
            ],
            [
             0.7777777777777778,
             "#fb9f3a"
            ],
            [
             0.8888888888888888,
             "#fdca26"
            ],
            [
             1,
             "#f0f921"
            ]
           ]
          },
          "colorway": [
           "#636efa",
           "#EF553B",
           "#00cc96",
           "#ab63fa",
           "#FFA15A",
           "#19d3f3",
           "#FF6692",
           "#B6E880",
           "#FF97FF",
           "#FECB52"
          ],
          "font": {
           "color": "#2a3f5f"
          },
          "geo": {
           "bgcolor": "white",
           "lakecolor": "white",
           "landcolor": "#E5ECF6",
           "showlakes": true,
           "showland": true,
           "subunitcolor": "white"
          },
          "hoverlabel": {
           "align": "left"
          },
          "hovermode": "closest",
          "mapbox": {
           "style": "light"
          },
          "paper_bgcolor": "white",
          "plot_bgcolor": "#E5ECF6",
          "polar": {
           "angularaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "radialaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "scene": {
           "xaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "yaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           },
           "zaxis": {
            "backgroundcolor": "#E5ECF6",
            "gridcolor": "white",
            "gridwidth": 2,
            "linecolor": "white",
            "showbackground": true,
            "ticks": "",
            "zerolinecolor": "white"
           }
          },
          "shapedefaults": {
           "line": {
            "color": "#2a3f5f"
           }
          },
          "ternary": {
           "aaxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "baxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           },
           "bgcolor": "#E5ECF6",
           "caxis": {
            "gridcolor": "white",
            "linecolor": "white",
            "ticks": ""
           }
          },
          "title": {
           "x": 0.05
          },
          "xaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          },
          "yaxis": {
           "automargin": true,
           "gridcolor": "white",
           "linecolor": "white",
           "ticks": "",
           "title": {
            "standoff": 15
           },
           "zerolinecolor": "white",
           "zerolinewidth": 2
          }
         }
        },
        "title": {
         "text": "US Treasury Term Structure"
        },
        "xaxis": {
         "anchor": "y",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          -1.3389485677083328,
          31.838948567708332
         ],
         "title": {
          "text": "Maturity"
         },
         "type": "linear"
        },
        "yaxis": {
         "anchor": "x",
         "autorange": true,
         "domain": [
          0,
          1
         ],
         "range": [
          -0.0004089171974522292,
          0.02320891719745223
         ],
         "tickformat": ".2%",
         "title": {
          "text": "SpotRate"
         },
         "type": "linear"
        }
       }
      },
      "image/png": "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"
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "TSDates = ['20200131','20200229','20200331','20200430','20200531','20200630']\n",
    "plotDF = TSdf.loc[TSdf[\"Date\"].isin(TSDates),:].reset_index(drop=True)\n",
    "plotDF[\"Date\"] = plotDF[\"Date\"].dt.date.astype(str)\n",
    "\n",
    "px.line(plotDF,x=\"Maturity\",y=\"SpotRate\",color=\"Date\",title=\"US Treasury Term Structure\")\\\n",
    ".update_layout(yaxis=dict(tickformat=\".2%\")).update_traces(mode='lines+markers')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "heading_collapsed": true
   },
   "source": [
    "## Background"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "hidden": true
   },
   "source": [
    "Let $\\mathbf{X}$ be an $n\\times k$ matrix whose columns are centered - i.e., the mean of each column is zero. Then the $k\\times k$ covariance matrix $\\mathbf{\\Sigma}$ is\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{\\Sigma} = \\frac{1}{n}\\mathbf{X'X}\n",
    "\\end{equation}\n",
    "\n",
    "We can diagonalize the covariance matrix by the similarity transformation\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{\\Sigma} = \\mathbf{U\\Lambda U'}\n",
    "\\end{equation}\n",
    "where\n",
    "* $\\mathbf{U}$ is a $k\\times k$ matrix whose columns are eigenvectors of $\\mathbf{\\Sigma}$\n",
    "* $\\mathbf{U}$ is an orthogonal matrix, $\\mathbf{UU'= U'U = I}$\n",
    "* $\\mathbf{\\Lambda}$ is a diagonal matrix consisting of the eigenvalues of $\\mathbf{\\Sigma}$\n",
    "\n",
    "In addition:\n",
    "\n",
    "* If $\\mathbf{\\Sigma}$ is real and symmetric, its eigenvalues are real\n",
    "* If the eigenvalues $\\lambda_i > 0 \\; \\forall\\, i$, then $\\mathbf{\\Sigma}$ is positive definite\n",
    "* If some $\\lambda_i = 0$, then $\\mathbf{\\Sigma}$ is positive semi-definite if the *non-zero* $\\lambda_i$ are greater than zero\n",
    "\n",
    "**Variation and reduction in dimensionality**\n",
    "\n",
    "$$\n",
    "\\text{Total variation} = \\sum_i \\sigma_i^2 = tr(\\mathbf{\\Sigma}) = tr(\\mathbf{\\Lambda}) = \\sum_i \\lambda_i\n",
    "$$\n",
    "where $tr(.)$ is the trace of a matrix and we have used the fact that $tr(\\mathbf{\\Sigma})=tr(\\mathbf{U\\Lambda U'})=tr(\\mathbf{U'U\\Lambda})=tr(\\mathbf{\\Lambda})$.\n",
    "\n",
    "The vectors in $\\mathbf{X}$ can be transformed to a new basis by post-multiplying them with the matrix $\\mathbf{U}$:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{P} = \\mathbf{X U}\n",
    "\\end{equation}\n",
    "\n",
    "The columns of $\\mathbf{P}$ are known as principal components. These components are orthogonal to each other. The $j$th principal component is \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{P}_j = \\mathbf{X}\\mathbf{U}_j\n",
    "\\end{equation}\n",
    "where $\\mathbf{U}_j$ is the $j$th column of $\\mathbf{U}$.\n",
    "\n",
    "The proportion of total variation explained by the $j$th principal component is $\\frac{\\lambda_i}{\\sum_i \\lambda_i}$. Often, a few principal components can account for a large fraction of the variation. Thus we may choose to ignore the eigenvectors corresponding to the smaller eigenvalues. This is what leads to **dimensionality reduction**.\n",
    "\n",
    "The matrix $\\mathbf{X}$ can be recovered by noting that $\\mathbf{X}=\\mathbf{PU'}$.\n",
    "\n",
    "**Relationship to Singular Value Decomposition (SVD)**\n",
    "\n",
    "Singular value decomposition is a non-unique decomposition of the matrix $\\mathbf{X}$ such that\n",
    "\n",
    "$$\n",
    "\\mathbf{X}_{n\\times k} = \\mathbf{V}_{n\\times n} \\mathbf{S}_{n\\times k} \\mathbf{U'}_{k\\times n}\n",
    "$$\n",
    "\n",
    "and \n",
    "* $\\mathbf{V, U}$ are unitary (orthogonal if $\\mathbf{X}$ is real)\n",
    "* $\\mathbf{S}$ is diagonal\n",
    "\n",
    "From this, we see that\n",
    "\n",
    "$$\n",
    "\\mathbf{\\Sigma} = \\frac{1}{n}\\mathbf{X'X} = \\frac{1}{n} \\mathbf{U\\,S\\,V'\\,V\\,S\\,U'} = \\frac{1}{n} \\mathbf{U\\, S^2\\, U'}\n",
    "$$\n",
    "\n",
    "which means that $\\frac{1}{n} \\mathbf{S^2} = \\mathbf{\\Lambda}$. Since $\\mathbf{S}$ is diagonal, it follows that\n",
    "\n",
    "$$\n",
    "\\frac{1}{n} s_i^2 = \\lambda_i\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Implementation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "from sklearn.decomposition import PCA\n",
    "np.set_printoptions(precision=3, suppress=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "test = plotDF.pivot(index='Date',columns='Maturity',values='SpotRate')\n",
    "Xdf = test.diff().dropna()\n",
    "X = Xdf.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "code_folding": []
   },
   "outputs": [],
   "source": [
    "#PCA code.  Steps\n",
    "# 1. Center X\n",
    "# 2. Compute Sigma = (1/n) X'X\n",
    "# 3. Compute eigenvalues and eigenvectors. \n",
    "# 4. Order eigenvalues by magnitude. Choose eigenvectors corresponding to a few of the largest eigenvalues.\n",
    "\n",
    "def myPCA(X):\n",
    "    X = X - np.mean(X,axis=0)\n",
    "    Sigma = np.cov(X,rowvar=False)\n",
    "\n",
    "    e,U = np.linalg.eigh(Sigma)    # eigenvalues and eigenvectors\n",
    "\n",
    "    OrderEV = np.argsort(e)[::-1]  # indices of eigenvalues sorted by magnitude. '[::-1]' reverses the vector.\n",
    "    l = e[OrderEV]\n",
    "    U = U[:,OrderEV]               # columns of U have to be ordered according to order of eigenvalues\n",
    "    PC = X @ U\n",
    "    return ((l,U,PC))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true,
     "source_hidden": true
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([95.059,  4.362,  0.444,  0.135,  0.   ,  0.   , -0.   , -0.   ])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[-0.564,  0.499,  0.34 , -0.023, -0.112,  0.341,  0.042,  0.432],\n",
       "       [-0.488,  0.273,  0.022, -0.047,  0.479, -0.319, -0.006, -0.594],\n",
       "       [-0.362, -0.046, -0.217, -0.041, -0.675, -0.497, -0.339, -0.003],\n",
       "       [-0.303, -0.17 , -0.434,  0.055, -0.228,  0.22 ,  0.75 , -0.159],\n",
       "       [-0.267, -0.186, -0.503,  0.35 ,  0.23 ,  0.443, -0.518,  0.041],\n",
       "       [-0.228, -0.4  , -0.096, -0.806,  0.247,  0.009, -0.052,  0.258],\n",
       "       [-0.238, -0.408,  0.18 ,  0.466,  0.295, -0.444,  0.197,  0.452],\n",
       "       [-0.203, -0.534,  0.595,  0.066, -0.221,  0.306, -0.105, -0.402]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.005,  0.003,  0.   , -0.   , -0.   ,  0.   , -0.   ,  0.   ],\n",
       "       [ 0.013, -0.002, -0.   ,  0.   ,  0.   , -0.   , -0.   , -0.   ],\n",
       "       [-0.006,  0.001, -0.   ,  0.   ,  0.   , -0.   ,  0.   , -0.   ],\n",
       "       [-0.006, -0.002,  0.001, -0.   , -0.   ,  0.   , -0.   ,  0.   ],\n",
       "       [-0.006, -0.001, -0.001, -0.   , -0.   ,  0.   ,  0.   ,  0.   ]])"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "l,U,PC = myPCA(X)\n",
    "(100*l)/sum(l)\n",
    "U\n",
    "PC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true,
    "jupyter": {
     "outputs_hidden": true
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[95.059  4.362  0.444  0.135  0.   ]\n",
      "[[-0.564 -0.488 -0.362 -0.303 -0.267 -0.228 -0.238 -0.203]\n",
      " [ 0.499  0.273 -0.046 -0.17  -0.186 -0.4   -0.408 -0.534]\n",
      " [ 0.34   0.022 -0.217 -0.434 -0.503 -0.096  0.18   0.595]\n",
      " [-0.023 -0.047 -0.041  0.055  0.35  -0.806  0.466  0.066]\n",
      " [ 0.258 -0.602  0.447  0.372 -0.437 -0.087  0.143 -0.116]]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[ 0.005,  0.003,  0.   , -0.   ,  0.   ],\n",
       "       [ 0.013, -0.002, -0.   ,  0.   ,  0.   ],\n",
       "       [-0.006,  0.001, -0.   ,  0.   ,  0.   ],\n",
       "       [-0.006, -0.002,  0.001, -0.   ,  0.   ],\n",
       "       [-0.006, -0.001, -0.001, -0.   ,  0.   ]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Comparison with scikit-learn PCA\n",
    "\n",
    "pca = PCA()          # Creating an object\n",
    "fit = pca.fit(X)\n",
    "print(100*fit.explained_variance_ratio_)\n",
    "print(fit.components_)                           # This is U'\n",
    "pca.fit_transform(X)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# PCA factors for US Treasury spot rate changes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "TSXdf = TSdf.pivot(index='Date',columns='Maturity',values='SpotRate').diff().dropna()\n",
    "TSX = TSXdf.values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.769 0.934 0.978 0.995 0.998 1.    1.    1.   ]\n"
     ]
    }
   ],
   "source": [
    "# Running PCA on the entire panel\n",
    "\n",
    "X = TSXdf.values\n",
    "dvec = TSXdf.index\n",
    "\n",
    "pca = PCA()          # Creating an object\n",
    "fit = pca.fit(X)\n",
    "\n",
    "evr = np.cumsum(fit.explained_variance_ratio_)\n",
    "PC = pd.DataFrame(pca.fit_transform(X), columns=['PC'+str(x) for x in range(pca.n_components_)])\n",
    "PC = pd.concat([pd.Series(dvec),PC],axis=1)\n",
    "\n",
    "print(evr)\n",
    "#PC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Save a 4 component factor model\n",
    "PC.iloc[:,0:5].to_pickle(\"s3://multifactor-etf/UST_PC4.pkl\")"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.3"
  },
  "toc": {
   "base_numbering": 1,
   "nav_menu": {},
   "number_sections": true,
   "sideBar": true,
   "skip_h1_title": false,
   "title_cell": "Table of Contents",
   "title_sidebar": "Contents",
   "toc_cell": false,
   "toc_position": {},
   "toc_section_display": true,
   "toc_window_display": false
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}