Description Usage Arguments Details Value Examples

GMM object

1 2 3 |

`model` |
A |

`data` |
A |

`model.type` |
A |

`compute.v` |
A |

`robust` |
A |

`eff` |
A |

`alpha` |
A |

`seed` |
A |

`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[(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*- "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 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 | ```
# AR
set.seed(1336)
n = 200
data = gen.gts(AR1(phi = .99, sigma2 = 0.01) + WN(sigma2 = 1), n)
# 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)
# ARMA case
set.seed(1336)
data = gen.gts(ARMA(ar = c(0.8897, -0.4858), ma = c(-0.2279, 0.2488),
sigma2 = 0.1796), 200)
#guided.arma = gmwm(ARMA(2,2), data, model.type="ssm")
adv.arma = gmwm(ARMA(ar=c(0.8897, -0.4858), ma = c(-0.2279, 0.2488), sigma2=0.1796),
data, model.type="ssm")
``` |

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