I am a forecasting professional and have recently started using R.

I'm currently trying to forecast this using this code:

`library(forecast) library(tseries) p=scan() #scans 54 variables p.ts=ts(p, frequency=12, start=c(2011, 01)) p.ts Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 2011 102.0 102.2 102.8 103.2 103.3 103.5 103.6 104.0 104.2 103.9 104.2 104.1 2012 104.5 104.8 104.9 105.3 105.5 105.5 105.4 105.1 105.6 105.8 106.3 106.4 2013 106.4 106.4 106.6 106.8 106.4 107.0 107.5 107.4 107.6 107.9 107.9 107.7 2014 107.8 108.1 108.2 108.9 108.7 109.0 109.1 109.4 109.1 109.9 109.8 109.9 2015 109.8 109.5 109.6 109.5 109.5 109.7 110.2 110.6 plot(p.ts) `

`plot(diff(p.ts)) `

Then I had a look at the ACF and PACF plots

It looks like a MA(1) process too. But not an AR process at all.

Hence, I chose to model it as ARIMA(0,1,1) process

`a=arima(p.ts, order=c(0,1,1)) summary(a) Call: arima(x = p.ts, order = c(0, 1, 1)) Coefficients: ma1 0.0757 s.e. 0.1119 sigma^2 estimated as 0.09556: log likelihood = -13.47, aic = 30.95 Training set error measures: ME RMSE MAE MPE MAPE MASE Training set 0.1450371 0.3066561 0.2472274 0.13619 0.2314932 0.9853266 ACF1 Training set -0.2479716 `

Then forecasted the numbers.

`f=forecast(a) plot(f) `

Can you help me understand where I went wrong? And how can I correct this?

This is one of five cases that I forecast. In such a case I generally model it with HoltWinters and get a decent response (one that comes very close to the realized values too).

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#### Best Answer

ARIMA(0,1,1) is a random walk with an MA(1) term on top. The forecast for a random walk is its last observed value, regardless of the forecast horizon. The forecast for an MA(1) process is nonzero only for horizon $h=1$. Thus you get a constant forecast (equal to the last observed value plus one value of MA(1) term) beyond $h=1$. This is what you see in the graph. Nothing wrong with it.

If you expect the upward-sloping linear time trend to continue, you could consider using a random walk model with positive drift. That would give you something more consistent with the historical trend.