Model Estimation

Model Estimation

This page documents the estimation parameters shared across ADAM and related functions. These parameters control the optimisation process, initial values, and advanced estimation options.

NLopt Optimizer Parameters

The smooth package uses NLopt for numerical optimisation. These parameters control the optimisation behaviour:

Parameter	R (via ...)	Python (via nlopt_kargs)	Default	Description
algorithm	Yes	Yes	"NLOPT_LN_NELDERMEAD"	Optimiser algorithm
maxeval	Yes	Yes	40×len(B)	Maximum evaluations
maxtime	Yes	Yes	None/1800s	Maximum time (seconds)
xtol_rel	Yes	Yes	1e-6	Relative parameter tolerance
xtol_abs	Yes	Yes	1e-8	Absolute parameter tolerance
ftol_rel	Yes	Yes	1e-8	Relative function tolerance
ftol_abs	Yes	Yes	0	Absolute function tolerance
print_level	Yes	Yes	0	Verbosity (0=silent, 3=detailed, 41=initials + final output)

The parameters are documented in the nlopt project.

R Usage

# Pass NLopt parameters via ...
model <- adam(y, model="AAN",
              algorithm="NLOPT_LN_SBPLX",
              maxeval=1000,
              maxtime=600,
              xtol_rel=1e-8,
              print_level=1)

Python Usage

# Pass NLopt parameters via nlopt_kargs dict
model = ADAM(model="AAN", nlopt_kargs={
             "algorithm": "NLOPT_LN_SBPLX",
             "maxeval": 1000,
             "maxtime": 600,
             "xtol_rel": 1e-8,
             "print_level": 1
})
model.fit(y)

Initial Parameter Vector (B)

B is the flat vector of all parameters passed to the optimizer. Providing it overrides the automatically computed starting point. Providing lb/ub replaces the automatically computed bounds entirely — the values are used as-is without adjustment.

The order of parameters in B depends on what the model estimates:

1. Smoothing parameters (alpha, beta, gamma, delta) — always first
2. Damping parameter (phi) — if a damped trend is used
3. ARMA coefficients — if ARIMA components are present
4. Initial ETS states (level, trend, seasonal) — only when initial="optimal" or "two-stage"
5. Initial ARIMA states — only when initial="optimal" or "two-stage"
6. External regressor coefficients — if regressors is not "complete"
7. Constant term — if included

With the default initial="backcasting", initial states are not in B, so for a simple AAN model B is just [alpha, beta].

R Usage

In R, B, lb, and ub are passed via ... to adam(). They are flat numeric vectors in the same order as B above.

# AAN with backcasting: B = [alpha, beta]
model <- adam(y, model="AAN",
              B=c(0.3, 0.1),   # starting point: alpha=0.3, beta=0.1
              lb=c(0, 0),      # lower bounds
              ub=c(1, 1))      # upper bounds

# ANA (no trend) with backcasting: B = [alpha, gamma]
model <- adam(y, model="ANA", lags=12,
              B=c(0.4, 0.2),
              lb=c(0.1, 0.05),
              ub=c(0.9, 0.5))

If B is outside the supplied bounds, R adjusts the bounds slightly to accommodate it.

Python Usage

In Python, pass B_initial, lb, and ub inside nlopt_kargs. When provided, they are used exactly as given — the internally computed starting point and bounds are not used.

# AAN with backcasting: B = [alpha, beta]
model = ADAM(model="AAN",
             nlopt_kargs={
                 "B_initial": [0.3, 0.1],   # starting point: alpha=0.3, beta=0.1
                 "lb": [0, 0],              # lower bounds
                 "ub": [1, 1],              # upper bounds
             })
model.fit(y)

# ANA (no trend) with backcasting: B = [alpha, gamma]
model = ES(model="ANA", lags=12,
           nlopt_kargs={
               "B_initial": [0.4, 0.2],
               "lb": [0.1, 0.05],
               "ub": [0.9, 0.5],
           })
model.fit(y)

You can supply only some of the three — for example, set bounds without fixing a starting point:

# Override only bounds, keep automatic starting point
model = ADAM(model="AAN",
             nlopt_kargs={"lb": [0.05, 0.01], "ub": [0.8, 0.4]})
model.fit(y)

See Bounds for details on parameter boundaries and stability restrictions.

Smoother Parameter

The smoother parameter controls how msdecompose smooths the time series for initialisation. Available options:

Value	R	Python	Description
"lowess"	Yes	Yes	LOcally WEighted Scatterplot Smoothing (default)
"ma"	Yes	Yes	Moving Average
"supsmu"	Yes	No	Friedman's SuperSmoother
"global"	Yes	Yes	Global mean (no smoothing)

R Usage

model <- adam(y, model="AAN", smoother="lowess")

Python Usage

model = ADAM(model="AAN", smoother="lowess")
model.fit(y)

See msdecompose for more details on the decomposition process.

Fisher Information

The Fisher Information matrix can be computed for uncertainty quantification.

Python: Not yet implemented.

Parameter	R	Python	Default	Description
FI	Yes	TBA	FALSE	Whether to compute Fisher Information matrix
stepSize	Yes	TBA	~1.22e-4	Step size for Hessian calculation

R Usage

model <- adam(y, model="AAN",
              FI=TRUE,
              stepSize=1e-5)

# Access Fisher Information
model$FI

The Fisher Information is used for computing standard errors and confidence intervals of parameters. This is done automatically by the vcov() method in R, see Coefficients-and-Parameters.

Backcasting Iterations

Backcasting is used to refine initial state estimates by iterating between forward and backward passes:

Parameter	R	Python	Default	Description
nIterations	Yes	-	2	Number of backcasting iterations
n_iterations	-	Yes	2	Number of backcasting iterations

R Usage

model <- adam(y, model="AAN", nIterations=5)

Python Usage

model = ADAM(model="AAN", n_iterations=5)
model.fit(y)

Higher values may improve initial state estimates but increase computation time.

Related Pages

• Initialisation - State initialisation methods
• Loss-Functions - Loss functions for estimation
• Bounds - Parameter bounds and stability
• ADAM - Main ADAM function documentation
• ES - Exponential Smoothing documentation