Performs estimation of time series models by using the GMWM estimator.
gmwm(
model,
data,
model.type = "imu",
compute.v = "auto",
robust = FALSE,
eff = 0.6,
alpha = 0.05,
seed = 1337,
G = NULL,
K = 1,
H = 100,
freq = 1
)A gmwm object with the structure:
estimate: Estimated Parameters Values from the GMWM Procedure
init.guess: Initial Starting Values given to the Optimization Algorithm
wv.empir: The data's empirical wavelet variance
ci_low: Lower Confidence Interval
ci_high: Upper Confidence Interval
orgV: Original V matrix
V: Updated V matrix (if bootstrapped)
omega: The V matrix inversed
obj.fun: Value of the objective function at Estimated Parameter Values
theo: Summed Theoretical Wavelet Variance
decomp.theo: Decomposed Theoretical Wavelet Variance by Process
scales: Scales of the GMWM Object
robust: Indicates if parameter estimation was done under robust or classical
eff: Level of efficiency of robust estimation
model.type: Models being guessed
compute.v: Type of V matrix computation
augmented: Indicates moments have been augmented
alpha: Alpha level used to generate confidence intervals
expect.diff: Mean of the First Difference of the Signal
N: Length of the Signal
G: Number of Guesses Performed
H: Number of Bootstrap replications
K: Number of V matrix bootstraps
model: ts.model supplied to gmwm
model.hat: A new value of ts.model object supplied to gmwm
starting: Indicates whether the procedure used the initial guessing approach
seed: Randomization seed used to generate the guessing values
freq: Frequency of data
A ts.model object containing one of the allowed models.
A matrix or data.frame object with only column
(e.g. \(N \times 1\)), a lts object,
or a gts object.
A string containing the type of GMWM needed:
"imu" or "ssm".
A string indicating the type of covariance matrix
solver. Valid values are:
"fast", "bootstrap",
"diag" (asymptotic diag),
"full" (asymptotic full). By default, the program
will fit a "fast" model.
A boolean indicating whether to use the robust
computation (TRUE) or not (FALSE).
A double between 0 and 1 that indicates the
efficiency.
A double between 0 and 1 that correspondings to the
\(\frac{\alpha}{2}\) value for the wavelet
confidence intervals.
An integer that controls the reproducibility of the
auto model selection phase.
An integer to sample the space for IMU and SSM
models to ensure optimal identitability.
An integer that controls how many times the
bootstrapping procedure will be initiated.
An integer that indicates how many different
samples the bootstrap will be collect.
A double that indicates the sampling frequency. By
default, this is set to 1 and only is important if GM()
is in the model
This function is under work. Some of the features are active. Others... Not so much.
The V matrix is calculated by: \(diag\left[ {{{\left( {Hi - Lo} \right)}^2}} \right]\).
The function is implemented in the following manner: 1. Calculate MODWT of data with levels = floor(log2(data)) 2. Apply the brick.wall of the MODWT (e.g. remove boundary values) 3. Compute the empirical wavelet variance (WV Empirical). 4. Obtain the V matrix by squaring the difference of the WV Empirical's Chi-squared confidence interval (hi - lo)^2 5. Optimize the values to obtain \(\hat{\theta}\) 6. If FAST = TRUE, return these results. Else, continue.
Loop k = 1 to K Loop h = 1 to H 7. Simulate xt under \(F_{\hat{\theta}}\) 8. Compute WV Empirical END 9. Calculate the covariance matrix 10. Optimize the values to obtain \(\hat{\theta}\) END 11. Return optimized values.
The function estimates a variety of time series models. If type = "imu" or "ssm", then parameter vector should indicate the characters of the models that compose the latent or state-space model. The model options are:
"AR1": a first order autoregressive process with parameters \((\phi,\sigma^2)\)
"GM": a guass-markov process \((\beta,\sigma_{gm}^2)\)
"ARMA": an autoregressive moving average process with parameters \((\phi _p, \theta _q, \sigma^2)\)
"DR": a drift with parameter \(\omega\)
"QN": a quantization noise process with parameter \(Q\)
"RW": a random walk process with parameter \(\sigma^2\)
"WN": a white noise process with parameter \(\sigma^2\)
If only an ARMA() term is supplied, then the function takes conditional least squares as starting values If robust = TRUE the function takes the robust estimate of the wavelet variance to be used in the GMWM estimation procedure.