DSCI 574: Spatial and Temporal Models
Model fitting and prediction in the presence of correlation due to temporal and/or spatial association. ARIMA models and Gaussian processes.
|#||Lab topic||Due Date|
|1||Use R to perform certain time series analyses including plots, smoothing, decomposition, computation of the sample autocorrelation function, lagging and differencing.||2019-02-09|
|2||Stochastic models for time series: simulation and model selection.||2019-02-16|
|3||Use R to select, fit and forecast based on the ARMA family of time series models.||2019-03-02|
|4||Explore visualization techniques for spatial data (R package gstat). Fit popular variogram models to spatial data; perform prediction using classical kriging.||2019-03-09|
|1||15:00 - 15:30||2019-02-27||In your lab section|
|2||10:00 - 10:30||2019-03-13||DPM 301|
|1||2019-02-05||Tue||Intro to time series; Chapter 1: Exploratory techniques in time series analysis|
|2||2019-02-07||Thur||Continuing Chapter 1: Exploratory techniques in time series analysis|
|3||2019-02-12||Tue||Chapter 2: Stochastic models for time series|
|4||2019-02-14||Thur||Continuing Chapter 2: Stochastic models for time series|
|5||2019-02-26||Tue||Chapter 3: Estimation and Model Fitting for Time Series|
|6||2019-02-28||Thur||Chapter 4: Prediction for Time Series|
|7||2019-03-05||Tue||Chapter 5: Spatial data and spatial processes|
|8||2019-03-07||Thur||Chapter 6: Methods for spatial prediction|
Course Learning Objectives
Chapter 1: Exploratory techniques in time series analysis
- Informally define and explain terminology used to describe time series, including trend, seasonal effects, cyclical effects, outlier and white noise.
- Recognize when curve–fitting may be an appropriate method for modelling a series.
- Describe models for seasonal variation, including additive and multiplicative models.
- Apply a filter (that is, a smoother) to a time series, centering if necessary.
- Use a filter to estimate the seasonal indices in a time series that has an additive seasonal component.
- Recognize the role of transformations for time series, and identify possible transformations to address certain features of series, such as a non-constant variance and multiplicative seasonal effects.
- Define the sample autocorrelation function and the correlogram.
- Describe the behaviour of the correlogram for series that alternate, have a trend or show seasonal fluctuations.
Chapter 2: Stochastic models for time series
- Define the autocovariance and autocorrelation functions for a time series model.
- Define and explain what it means to say that a process is (weakly) stationary.
- Define what is meant by a white noise process.
- Define a moving average process of order q, i.e., an MA(q) .
- Derive the mean, variance and autocovariance function of a stationary MA(q) process.
- Define the notion of invertibility of a process.
- Define an autoregressive process of order p, i.e., an AR(p) .
- Derive properties for an AR(1) , including the mean, variance and autocorrelation function.
- Define when an AR(p) is stationary.
- Define an ARMA(p, q) process and state conditions when an ARMA(p, q) process is stationary and/or invertible.
Chapter 3: Estimation and model fitting for time series
- Given a class of ARMA models, list the main steps for fitting a suitable model to the data.
- Describe estimation of the mean of the process, and of its autocovariance and autocorrelation functions. Know their statistical properties.
- Use the correlogram to decide which model from the ARMA family is suitable for the data.
- For an AR model, describe how to select the order of the process using the partial autocorrelation function and how to fit the remaining model parameters.
- For an MA process, be able to determine the order of the process and describe how to carry parameter estimation.
- Use the correlogram to identify situations when an ARMA model is suitable, and use software to fit the model.
- Apply model-selection criteria to choose among possible models.
Chapter 4: Prediction for time series
- Describe how exponential smoothing technique can be used to make forecasts for stationary time series data.
- Outline the steps of Box-Jenkins forecasting procedure.
- Compute Box-Jenkins forecasts using the model equation.
- Use the MA representation of the model to construct prediction intervals for the forecasts.
Chapter 5: Spatial data and spatial processes
- Use tools in R package gstat to visualize point referenced spatial data and identify its features to guide subsequent modelling.
- Define a spatial random field and describe its possible representation in terms of an overall spatial trend plus a process having a spatial structure.
- Define second-order and isotropic stationarity.
- Define a Gaussian random field.
- Define a variogram and covariance function, and recognize their role as measures of dependence over space.
Chapter 6: Methods for spatial prediction
- Fit popular variogram models to spatial data and explain features such as the nugget, sill and range.
- Understand when a linear spatial predictor is appropriate. Apply classical kriging to make spatial predictions.
- Be familiar with modern methods of spatial prediction such as Bayesian kriging.
- Shaddick, Gavin and Zidek, James V. Spatio-Temporal Methods in Environmental Epidemiology. CRC Press, 2016.
- Chatfield, Chris. The Analysis of Time Series: An Introduction. CRC Press, 2003.