This data is weekly exchange rate data for US/Euro (number of USD per one Euro). I downloaded it from the FRED database.

Setup

library(forecast)
## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(nnet)

Data

ts = ts(exchangerate[,2], frequency = 52, start = c(2010,01))
autoplot(ts, main = "US/Euro Exchange Rate", ylab = 'USD per one Euro')

pacf(ts)

acf(ts)

Split data

train = head(ts, n = length(ts)-102)
test = tail(ts, n = 102)

Neural Net

mod = nnetar(train, lambda=0)
fc = forecast(mod,h=104)
autoplot(fc)

checkresiduals(fc)
## Warning in modeldf.default(object): Could not find appropriate degrees of
## freedom for this model.

Logged Data

logtrain = log(train)
logtest = log(test)

logmod = nnetar(logtrain, lambda=0)
logfc = forecast(logmod,h=104)
autoplot(logfc)

checkresiduals(logfc)
## Warning in modeldf.default(object): Could not find appropriate degrees of
## freedom for this model.

Accuracy

accuracy(fc, test)
##                        ME       RMSE         MAE          MPE      MAPE
## Training set 5.660867e-05 0.01166770 0.009119122 -0.004302022 0.7392899
## Test set     1.427187e-02 0.02233122 0.018695844  1.249033950 1.6558268
##                   MASE       ACF1 Theil's U
## Training set 0.1027375 0.01205408        NA
## Test set     0.2106304 0.82504744   2.65278
accuracy(logfc, logtest)
##                        ME        RMSE         MAE        MPE      MAPE
## Training set 0.0003529884 0.009105124 0.007222734 -0.1921338  4.526529
## Test set     0.0002676407 0.018458234 0.015192477 -2.4668969 14.153117
##                   MASE        ACF1 Theil's U
## Training set 0.1015120 0.008038891        NA
## Test set     0.2135229 0.888436677  2.666307

The accuracy information shows that both models perform pretty well. While using the logged data makes a slight difference in the model chosen by the neural net, the forecast plots looks pretty similar, and this is confirmed in the accuracy data. The raw data performs slightly better, and neither model has all that much bias. We do see some autocorrelation in both models.