The Lynx Data Set - Assignment Example

It would have been impossible to produce any of the needed outputs; graphical and Word.

ARMA stands for Autoregressive Moving Average models. It is a mixed model that comprises the Autoregressive model (AR), and the Moving Average model (MA). The AR has the function:

where αi’s denote the autocorrelation coefficient at respective lags (Khashei & Bijari, 2010).

On its part, the MA model follows the function:

where βi’s denote the weights for preceding values of the time series.

ARIMA stands for the integrated autoregressive moving average model. It predicts expected future values of a time series by use of the available past values. It has the function:

where t is the time index, B is the backshift operator defined as is a differenced series response, μ is the intercept, and, the AR operator and the MA operator wrote and

are the sequence of error terms.

Features of Lynx Data Set Tested Using ARMA and ARIMA:

The Code:

?lynx

> ts(lynx)

acf(lynx)

fit1=arima(lynx,order=c(1,0,0))

fit2=arima(lynx,order=c(0,1,1))

fit3=arima(lynx,order=c(1,1,1))

fit4=arima(lynx,order=c(0,0,1))

fit5=arima(lynx,order=c(1,0,1))

predict(fit4,n.ahead=10)

#filtering

lynx<-filter(lynx,side=2,rep(1,50)/50)#Filters Data

lynx

line(time,lynx)

plot(time,lynx)#Plots the Filtered Data

Z=ts(1056.207: 1348.230: 1348.230: 1348.230: 1348.230: 1348.230: 1348.230: 1348.230:

 1348.230: 1348.230)

line(Z)

plot (line(Z))

The Output and Comment on Features:

A Hot-Winters exponential smoothing can not be applied since the time series plot of this additive model does not exhibit either an increasing or a decreasing trend, save for the seasonality.

This is an ACF plot of the lynx data set. It exhibits an alternating pattern like the data set. The plot exhibits a dying-off trend, which points to an autoregressive (AR) model.

Above is the plot of the PACF of the lynx data set. From this PACF, we notice that a sharp cut-off lends at point 2, therefore we consider the lynx data set to have the qualities of an autoregressive model of order 2, AR (2).

From the ACF and PACF, we conclude that the best model for this data would be ARMA (2,0). It is impossible to reduce the AR value, the observed cut-off point, but since there is no indication of an MA cut-off, we assign MA the value 0. The best model keeps the least possible number of values.

The forecast values:

1056.207, 1348.230, 1348.230, 1348.230, 1348.230, 1348.230, 1348.230, 1348.230,

 1348.230 and 1348.230.