Index of US Industrial Production

Description

Index of US industrial production (1985 = 100).

Usage

data("USProdIndex")

Format

A quarterly multiple time series from 1960(1) to 1981(4) with 2 variables.

unadjusted

raw index of industrial production,

adjusted

seasonally adjusted index.

Source

Online complements to Franses (1998).

http://www.few.eur.nl/few/people/franses/research/book2.htm

References

Franses, P.H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.

See Also

Franses1998

Examples

data("USProdIndex")
plot(USProdIndex, plot.type = "single", col = 1:2)

## EACF tables (Franses 1998, p. 99)
ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
ddiff <- function(x) diff(diff(x, frequency(x)), 1)
eacf <- function(y, lag = 12) {
  stopifnot(all(lag > 0))
  if(length(lag) < 2) lag <- 1:lag
  rval <- sapply(
    list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
         Dy = diff(y, frequency(y)), dDy = ddiff(y)),
    function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
  rownames(rval) <- lag
  return(rval)
}

## Franses (1998), Table 5.1
round(eacf(log(USProdIndex[,1])), digits = 3)

## Franses (1998), Equation 5.6: Unrestricted airline model
## (Franses: ma1 = 0.388 (0.063), ma4 = -0.739 (0.060), ma5 = -0.452 (0.069))
arima(log(USProdIndex[,1]), c(0, 1, 5), c(0, 1, 0), fixed = c(NA, 0, 0, NA, NA))

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
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> library(AER)
Loading required package: car
Loading required package: lmtest
Loading required package: zoo

Attaching package: 'zoo'

The following objects are masked from 'package:base':

    as.Date, as.Date.numeric

Loading required package: sandwich
Loading required package: survival
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/AER/USProdIndex.Rd_%03d_medium.png", width=480, height=480)
> ### Name: USProdIndex
> ### Title: Index of US Industrial Production
> ### Aliases: USProdIndex
> ### Keywords: datasets
> 
> ### ** Examples
> 
> data("USProdIndex")
> plot(USProdIndex, plot.type = "single", col = 1:2)
> 
> ## EACF tables (Franses 1998, p. 99)
> ctrafo <- function(x) residuals(lm(x ~ factor(cycle(x))))
> ddiff <- function(x) diff(diff(x, frequency(x)), 1)
> eacf <- function(y, lag = 12) {
+   stopifnot(all(lag > 0))
+   if(length(lag) < 2) lag <- 1:lag
+   rval <- sapply(
+     list(y = y, dy = diff(y), cdy = ctrafo(diff(y)),
+          Dy = diff(y, frequency(y)), dDy = ddiff(y)),
+     function(x) acf(x, plot = FALSE, lag.max = max(lag))$acf[lag + 1])
+   rownames(rval) <- lag
+   return(rval)
+ }
> 
> ## Franses (1998), Table 5.1
> round(eacf(log(USProdIndex[,1])), digits = 3)
       y     dy    cdy     Dy    dDy
1  0.975  0.162  0.242  0.851  0.535
2  0.947  0.140  0.196  0.586  0.162
3  0.918 -0.110 -0.061  0.295 -0.051
4  0.888  0.300  0.205  0.036 -0.328
5  0.853 -0.268 -0.264 -0.126 -0.296
6  0.821 -0.046 -0.032 -0.220 -0.190
7  0.789 -0.249 -0.224 -0.274 -0.165
8  0.761  0.120  0.008 -0.296 -0.204
9  0.732 -0.257 -0.253 -0.262 -0.066
10 0.705  0.015  0.044 -0.207  0.080
11 0.676 -0.198 -0.165 -0.172  0.025
12 0.649  0.199  0.099 -0.138  0.018
> 
> ## Franses (1998), Equation 5.6: Unrestricted airline model
> ## (Franses: ma1 = 0.388 (0.063), ma4 = -0.739 (0.060), ma5 = -0.452 (0.069))
> arima(log(USProdIndex[,1]), c(0, 1, 5), c(0, 1, 0), fixed = c(NA, 0, 0, NA, NA))

Call:
arima(x = log(USProdIndex[, 1]), order = c(0, 1, 5), seasonal = c(0, 1, 0), 
    fixed = c(NA, 0, 0, NA, NA))

Coefficients:
         ma1  ma2  ma3      ma4      ma5
      0.4603    0    0  -0.7731  -0.5313
s.e.  0.0707    0    0   0.0626   0.0713

sigma^2 estimated as 0.0003366:  log likelihood = 314.84,  aic = -621.69
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>