gmwm | R Documentation |

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
)
```

`model` |
A |

`data` |
A |

`model.type` |
A |

`compute.v` |
A |

`robust` |
A |

`eff` |
A |

`alpha` |
A |

`seed` |
An |

`G` |
An |

`K` |
An |

`H` |
An |

`freq` |
A |

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.

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 gmwmmodel.hat: A new value of

`ts.model`

object supplied to gmwmstarting: Indicates whether the procedure used the initial guessing approach

seed: Randomization seed used to generate the guessing values

freq: Frequency of data

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