The product and ratio models from coherentfdm are forecast, and
the results combined to give forecasts for each group in the original data.
Usage
# S3 method for class 'fdmpr'
forecast(object, h = 50, level = 80, K = 100, drange = c(0, 0.5), ...)Arguments
- object
Output from
coherentfdm.- h
Forecast horizon.
- level
Confidence level for prediction intervals.
- K
Maximum number of years to use in forecasting coefficients for ratio components.
- drange
Range of fractional differencing parameter for the ratio coefficients.
- ...
Other arguments as for
forecast.fdm.
Value
Object of class fmforecast2 containing a list of objects each
of class fmforecast. The forecasts for each group in the original
data are given first. Then the forecasts from the product model, and
finally a list of forecasts from each of the ratio models.
Examples
fr.short <- extract.years(fr.sm, 1950:2006)
fr.fit <- coherentfdm(fr.short)
fr.fcast <- forecast(fr.fit)
plot(fr.fcast$male)
plot(fr.fcast$ratio$male, plot.type = "component", components = 3)
models(fr.fcast)
#>
#> ************* PRODUCT MODEL *************
#>
#> -- Coefficient 1 --
#> Series: xx[, i]
#> ARIMA(1,1,0) with drift
#>
#> Coefficients:
#> ar1 drift
#> -0.4250 -0.2098
#> s.e. 0.1206 0.0228
#>
#> sigma^2 = 0.06039: log likelihood = 0.05
#> AIC=5.89 AICc=6.36 BIC=11.97
#>
#> -- Coefficient 2 --
#> Series: xx[, i]
#> ARIMA(0,1,0)
#>
#> sigma^2 = 0.01882: log likelihood = 31.78
#> AIC=-61.56 AICc=-61.48 BIC=-59.53
#>
#> -- Coefficient 3 --
#> Series: xx[, i]
#> ARIMA(1,0,0) with zero mean
#>
#> Coefficients:
#> ar1
#> 0.9518
#> s.e. 0.0449
#>
#> sigma^2 = 0.02409: log likelihood = 24.63
#> AIC=-45.27 AICc=-45.04 BIC=-41.18
#>
#> -- Coefficient 4 --
#> Series: xx[, i]
#> ARIMA(0,0,0) with zero mean
#>
#> sigma^2 = 0.03996: log likelihood = 10.89
#> AIC=-19.78 AICc=-19.71 BIC=-17.74
#>
#> -- Coefficient 5 --
#> Series: xx[, i]
#> ARIMA(1,0,2) with zero mean
#>
#> Coefficients:
#> ar1 ma1 ma2
#> 0.8425 -0.6319 0.3379
#> s.e. 0.1173 0.1584 0.1432
#>
#> sigma^2 = 0.01901: log likelihood = 33.08
#> AIC=-58.15 AICc=-57.38 BIC=-49.98
#>
#> -- Coefficient 6 --
#> Series: xx[, i]
#> ARIMA(2,0,2) with zero mean
#>
#> Coefficients:
#> ar1 ar2 ma1 ma2
#> 1.8493 -0.9078 -1.3057 0.4781
#> s.e. 0.0705 0.0663 0.1613 0.1487
#>
#> sigma^2 = 0.005993: log likelihood = 66.08
#> AIC=-122.16 AICc=-120.99 BIC=-111.95
#>
#>
#>
#> ************* RATIO MODELS *************
#>
#>
#> *********** FEMALE ***********
#>
#>
#> -- Coefficient 1 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ma.ma1 ma.ma2
#> 0.4090936 -1.1513350 -0.5306586
#> sigma[eps] = 0.1303427
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 2 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ma.ma1 ma.ma2
#> 4.583013e-05 -1.622329e-01 5.425798e-01
#> sigma[eps] = 0.1459614
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 3 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ar.ar1 ma.ma1
#> 4.583013e-05 9.798979e-01 4.156993e-01
#> sigma[eps] = 0.06410902
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 4 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ar.ar1 ar.ar2 ma.ma1 ma.ma2
#> 0.3913578 1.6048157 -0.7526423 1.6155005 -0.9998107
#> sigma[eps] = 0.06159422
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 5 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> Coefficients:
#> d ar.ar1
#> 4.583013e-05 7.006761e-01
#> sigma[eps] = 0.06151039
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 6 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ar.ar1 ma.ma1
#> 4.583013e-05 8.123545e-01 3.577327e-01
#> sigma[eps] = 0.05375933
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#>
#>
#> *********** MALE ***********
#>
#>
#> -- Coefficient 1 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ma.ma1 ma.ma2
#> 0.4236553 -1.1435894 -0.5225683
#> sigma[eps] = 0.1209133
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 2 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ma.ma1 ma.ma2
#> 4.583013e-05 -1.622329e-01 5.425798e-01
#> sigma[eps] = 0.1425088
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 3 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ar.ar1 ma.ma1
#> 4.583013e-05 9.798979e-01 4.156993e-01
#> sigma[eps] = 0.06414137
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 4 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> Coefficients:
#> d ar.ar1 ar.ar2 ma.ma1 ma.ma2
#> 0.3797002 1.6131684 -0.7587267 1.6171315 -0.9999822
#> sigma[eps] = 0.06278872
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 5 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> Coefficients:
#> d ar.ar1
#> 4.583013e-05 7.006761e-01
#> sigma[eps] = 0.06202872
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"
#>
#> -- Coefficient 6 --
#>
#> Call:
#> arfima(y = xx[, i], drange = ..2, estim = "mle")
#>
#> *** Warning during (fdcov) fit: unable to compute correlation matrix; maybe change 'h'
#>
#> Coefficients:
#> d ar.ar1 ma.ma1
#> 4.583013e-05 8.123545e-01 3.577327e-01
#> sigma[eps] = 0.05376532
#> a list with components:
#> [1] "log.likelihood" "n" "msg" "d"
#> [5] "ar" "ma" "covariance.dpq" "fnormMin"
#> [9] "sigma" "stderror.dpq" "correlation.dpq" "h"
#> [13] "d.tol" "M" "hessian.dpq" "length.w"
#> [17] "residuals" "fitted" "call" "x"
#> [21] "series"