Interpolation of an Atypical Frequency Series by Regression Models.

Perform temporal interpolation of low-frequency to high-frequency time series by regression models. The implemented models include Chow-Lin, Fernandez, Litterman and some variants of those algorithms. The temporal_interpolation_raw() function extends temporal_interpolation() by allowing temporal interpolation for any frequency ratio.

Usage

temporal_interpolation_raw(
  series,
  constant = TRUE,
  trend = FALSE,
  indicators = NULL,
  startoffset = 0L,
  model = c("Ar1", "Rw", "RwAr1"),
  freqratio,
  obsposition = -1L,
  rho = 0,
  rho.fixed = FALSE,
  rho.truncated = 0,
  zeroinitialization = FALSE,
  diffuse.algorithm = c("SqrtDiffuse", "Diffuse", "Augmented"),
  diffuse.regressors = FALSE,
  nbcsts = 0L,
  nfcsts = 0L
)

Arguments

series: A low-frequency time series to be interpolated. It must be a numeric vector.
constant: Boolean. Indicates whether a constant term is included in the model. The default is TRUE. Note that this argument is used only with model = "Ar1" when zeroinitialization = FALSE. For additional information, see the package vignette.
trend: Boolean. Indicates whether a linear trend is included in the model. The default is FALSE.
indicators: One or more high‑frequency indicator series used in the interpolation. If NULL (the default), no indicator is used. When provided, the argument must be a numeric vector or a matrix.
startoffset: The number of initial observations in the indicator series that precede the start of the low-frequency series. The value must be either 0 or a positive integer (default is 0). This argument is ignored when no indicator is provided.
model: A character string specifying the model of the error term at the disaggregated level. The options are: "Ar1" (Chow Lin), "Rw" (Fernandez), and "RwAr1" (Litterman).
freqratio: An integer specifying the frequency ratio between the interpolated series and the low-frequency series. This argument is mandatory and must be a positive integer.
obsposition: An integer specifying the position of the low-frequency observations within the interpolated series (e.g. the 1st month of the year, the 2d month, etc.). The value must be a positive integer or -1 (the default).The default value is equivalent to setting the value of the parameter equal to the frequency of the series, meaning that the last value of the interpolated series is consistent with the low-frequency series.
rho: A numeric value giving the (initial) value of the autoregressive parameter. This argument is used only for "Ar1" and "RwAr1" models.
rho.fixed: Boolean. Specifies whether the supplied value of rho is fixed. The default is FALSE, which indicates that rho is estimated.
rho.truncated: A numeric value defining the lower bound of the admissible range for rho. The evaluation range is [rho.truncated, 1[.
zeroinitialization: Boolean. If TRUE, the initial values of the autoregressive model are set to zero. The default is FALSE.
diffuse.algorithm: A character string specifying the algorithm used for diffuse initialization. The default is "SqrtDiffuse".
diffuse.regressors: Boolean. Indicates whether the coefficients of the regression model are treated as diffuse (TRUE) or as fixed unknown (FALSE, the default).
nbcsts: An integer specifying the number of backcast periods. This argument is ignored when one or more indicator series is provided.
nfcsts: An integer specifying the number of forecast periods. This argument is ignored when one or more indicator series is provided.

Value

An object of class "JD3_INTERPRAW_RSLTS" containing the results of the temporal interpolation procedure.

Examples

# Use of Chow-lin method to interpolate a biennial series with an annual
# indicator (the low-frequency series is consistent with the last value of the
# interpolated series)
Y <- stats::aggregate(rjd3toolkit::Retail$RetailSalesTotal, 0.5)
x <- stats::aggregate(rjd3toolkit::Retail$FoodAndBeverageStores, 1)
ti <- temporal_interpolation_raw(as.numeric(Y), indicators = as.numeric(x), freqratio = 2)
ti$estimation$interp
#>  [1] 3757964 4324395 4332525 4655006 4840668 5050272 5395661 5556665 6056481
#> [10] 6155126 6402476 6402063 7177121 7105610 7885934 7936844 7591404 8389142
#> [19] 8654201

# Use of Fernandez method to interpolate a series without indicator
# considering a frequency ratio of 5 (the low-frequency series is consistent
# with the last value of the interpolated series). For example, Y2 could be a
# quinquennial series to interpolate annually.
Y2 <- c(500,510,525,520)
ti2 <- temporal_interpolation_raw(Y2, model = "Rw", freqratio = 5, nbcsts = 1, nfcsts = 2)
ti2$estimation$interp
#>  [1] 500 500 502 504 506 508 510 513 516 519 522 525 524 523 522 521 520 520 520

# Same with an indicator, considering an offset in the latter
Y2 <- c(500,510,525,520)
x2 <- c(485,
        490, 492.5, 497.5, 520, 495,
        500, 502.5, 505, 527.5, 515,
        522.5, 517.5, 522.5, 545, 520,
        535, 515, 540, 565, 550)
ti3 <- temporal_interpolation_raw(Y2, indicators = x2, startoffset = 1, model = "Rw", freqratio = 5)
ti3$estimation$interp
#>  [1] 497.5410 500.0000 502.2459 505.7213 517.8033 506.5246 510.0000 512.0164
#>  [9] 514.0328 525.8852 520.5246 525.0000 520.3115 520.5410 529.3770 514.8525
#> [17] 520.0000 510.1639 522.4590 534.7541 527.3770

# Same considering that the first value of the interpolated series is the one
# consistent with the low-frequency series
ti4 <- temporal_interpolation_raw(Y2, indicators = x2, startoffset = 1,
                                  model = "Rw", freqratio = 5, obsposition = 1)
ti4$estimation$interp
#>  [1] 497.5410 500.0000 502.2459 505.7213 517.8033 506.5246 510.0000 512.0164
#>  [9] 514.0328 525.8852 520.5246 525.0000 520.3115 520.5410 529.3770 514.8525
#> [17] 520.0000 510.1639 522.4590 534.7541 527.3770

Usage

Arguments

Value

See also

Examples