tcs_decomp_estim: Trend cycle seasonal decomposition using the Kalman filter.

In opendoor-labs/TCSDecomp: Structrual time series decomposition using the Kalman filter

Description

Estimates a structural time series model using the Kalman filter and maximum likelihood. The seasonal and cycle components are assumed to be of a trigonometric form. The function checks three trend specifications to decompose a univariate time series into trend, cycle, and/or seasonal components plus noise. The function automatically detects the frequency and checks for a seasonal and cycle component if the user does not specify the frequency or decomposition model. This can be turned off by setting freq or specifying decomp. State space model for decomposition follows Yt = T_t + C_t + S_t + BX_t + e_t, e_t ~ N(0, sig_e^2) Y is the data T is the trend component C is the cycle component S is the seasonal component X is the exogenous data with parameter vector B e is the observation error

Usage

tcs_decomp_estim(
  y,
  exo = NULL,
  freq = NULL,
  decomp = NULL,
  trend_spec = NULL,
  multiplicative = NULL,
  par = NULL,
  harmonics = NULL,
  det_obs = F,
  det_trend = F,
  det_seas = F,
  det_cycle = F,
  det_drift = F,
  wavelet.method = "ARIMA",
  wavelet.sim = 100,
  level = 0.01,
  optim_methods = c("BFGS", "NM", "CG", "SANN"),
  maxit = 10000,
  verbose = F
)

Arguments

y	Univariate time series of data values. May also be a 2 column data frame containing a date column.
exo	Matrix of exogenous variables. Can be used to specify regression effects or other seasonal effects like holidays, etc.
freq	Frequency of the data (1 (yearly), 4 (quarterly), 12 (monthly), 52 (weekly), 365 (daily)), default is NULL and will be automatically detected
decomp	Decomposition model ("tend-cycle-seasonal", "trend-seasonal", "trend-cycle", "trend-noise")
trend_spec	Trend specification ("rw", "rwd", "2rw"). The default is NULL which will choose the best of all specifications based on the maximum likielhood. "rw" is the random walk trend. "rwd" is the random walk with random walk drift trend. "2rw" is a 2nd order random walk trend.
multiplicative	If data should be logged to create a multiplicative model
par	Initial parameters, defalut is NULL
harmonics	The seasonal harmonics to include, default is NULL which results in unique(1:floor(seasons/2))
det_obs	Set the observation equation error variance to 0 (deterministic observation equation)
det_trend	Set the trend error variance to 0 (deterministic trend)
det_seas	Set the seasonality error variances to 0 (deterministic seasonality)
det_cycle	Set thecycle error variance to 0 (deterministic cycle)
det_drift	Set the drift error variance to 0 (deterministic drift)
wavelet.method	Method for wavelet analysis comparison ("white.nose", "shuffle", "Fourier.rand", "AR", "ARIMA"). Default is "ARIMA".
wavelet.sim	Number of simulations for wavelet analysis. Default is 100
optim_methods	Vector of 1 to 3 optimization methods in order of preference ("NR", "BFGS", "CG", "BHHH", or "SANN")
maxit	Maximum number of iterations for the optimization

Value

List of estimation values including coefficients, convergence code, datea frequency, decomposition used, and trend specification selected.

Author(s)

Alex Hubbard ([e-mail])

Examples

tcs_decomp_estim(y = DT[, c("date", "y")])
If multiplicative = T, then the data is logged and the original model becomes multiplicative (Y_t = T_t * C_t * S_t * BX_t * e_t)
If trend is "rw", the trend model is T_t = T_{t-1} + e_t, e_t ~ N(0, sig_t^2)
If trend is "rwd", the trend model is T_t = M_{t-1} + T_{t-1} + e_t, e_t ~ N(0, sig_t^2) with 
     M_t = M_{t-1} + n_t, n_t ~ N(0, sig_m^2) where
If trend is "2rw", the trend model is T_t = 2T_{t-1} - T_{t-2} + e_t, e_t ~ N(0, sig_t^2)
If det_obs = T then sig_e is set to 0 
If det_trend = T then the variacne of the trend (sig_t) is set to 0 and is referred to as a smooth trend
If det_drift = T then the variance of the drift (sig_m) is set to 0 and is refereed to as a deterministic drift
If det_seas = T then the variance all seasonality frequencies j (sig_s) are set to 0 and is referred to as deterministic seasonality
If det_cycle = T then the variance of the cyclce (sig_c) is set to 0 and is refreed to as a deterministic cycle

opendoor-labs/TCSDecomp documentation built on April 21, 2020, 3:15 a.m.