mgmwm: Multivariate Generalized Method of Wavelet Moments (MGMWM)...
In SMAC-Group/mgmwm: Multisignal GMWM

Description Usage Arguments Details Value Examples

View source: R/mgmwm.R

Performs estimation of time series models by using the GMWM estimator.

mgmwm(
  mimu,
  model = NULL,
  CI = FALSE,
  alpha_ci = NULL,
  n_boot_ci_max = NULL,
  stationarity_test = FALSE,
  B_stationarity_test = 30,
  alpha_near_test = NULL,
  seed = 2710
)

`mimu`	A `mimu` object.
`model`	A `ts.model` object containing one of the allowed models.
`CI`	A `bolean` to compute the confidence intervals for estimated parameters.
`alpha_ci`	A `double` between 0 and 1 that correspondings to the alpha/2 value for the parameter confidence intervals.
`n_boot_ci_max`	A `double` representing the maximum number of bootstrap replicates for parameters confidence intervals computaion.
`stationarity_test`	A `bolean` to compute the near-stationarity test.
`B_stationarity_test`	A `double` representing the number of bootstrap replicates. for near-stationarity test computation.
`alpha_near_test`	A `double` between 0 and 1 that correspondings to the rejection region for the p value in the near-stationarity test
`seed`	An `integer` that controls the reproducibility of the auto model selection phase.

This function is under work. Some of the features are active. Others... Not so much.

The V matrix is calculated by: diag[(Hi-Lo)^2].

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 theta^hat 6. If FAST = TRUE, return these results. Else, continue.

Loop k = 1 to K Loop h = 1 to H 7. Simulate xt under F_theta^hat 8. Compute WV Empirical END 9. Calculate the covariance matrix 10. Optimize the values to obtain theta^hat 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
"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

A mgmwm object with the structure:

estimates: Estimated Parameters Values from the MGMWM Procedure
wv_empir: The data's empirical wavelet variance
ci_low: Lower Confidence Interval
ci_high: Upper Confidence Interval
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
model.type: Models being guessed
alpha: Alpha level used to generate confidence intervals
model: ts.model supplied to gmwm
model.hat: A new value of ts.model object supplied to gmwm

# AR
set.seed(1336)
n = 200
data = gen_gts(n, AR1(phi = .99, sigma2 = 0.01) + WN(sigma2 = 1))

# Models can contain specific parameters e.g.
adv.model = gmwm(AR1(phi = .99, sigma2 = 0.01) + WN(sigma2 = 0.01),
                            data)

# Or we can guess the parameters:
guided.model = gmwm(AR1() + WN(), data)

# Want to try different models?
guided.ar1 = gmwm(AR1(), data)

# Faster:
guided.ar1.wn.prev = update(guided.ar1, AR1()+WN())

# OR

# Create new GMWM object.
# Note this is SLOWER since the Covariance Matrix is recalculated.
guided.ar1.wn.new = gmwm(AR1()+WN(), data)