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I've created an Arima model based on past forex closing prices using auto arima, which has generated a (0,1,0) ARIMA model.

> auto.arima(ma5)
Series: ma5 
ARIMA(0,1,0)                    

sigma^2 estimated as 5.506e-07:  log likelihood=11111.42
AIC=-22220.83   AICc=-22220.83   BIC=-22215.27

I next tried to plot the forecasted values, but as you can see all predictions are constant. Anyone know what I'm doing wrong?

enter image description here

AkshaiShah
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    There's nothing wrong. The upcoming expected value from an ARIMA(0,1,0) process is equal to the last observed value. – Richard Hardy Jan 30 '15 at 12:20
  • @RichardHardy Is that only true for stationary series? (I am not a time series expert, but that seems logical to me). – Peter Flom Jan 30 '15 at 12:38
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    ARIMA(0,1,0) is a non-stationary time series. It is just a random walk, i.e. a cumulative sum of *innovations* or *shocks*. Since the expected value of a new *innovation* is zero, the expected cumulative sum one period ahead is just the current value of the cumulative sum. Therefore, the forecast is equal to the last observed value. Meanwhile, a forecast for a stationary time series will almost never be equal to the last observation (although there may be some special cases). – Richard Hardy Jan 30 '15 at 12:55
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    Including a drift may capture some trending pattern. See argument `include.drift` in `forecast::Arima` and apply `forecast` on the fitted model. – javlacalle Jan 30 '15 at 13:28
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    See [here](http://stats.stackexchange.com/questions/125909), [here](http://stats.stackexchange.com/questions/68379), [here](http://stats.stackexchange.com/questions/84255), [here](http://stats.stackexchange.com/questions/124000), & [here](http://stats.stackexchange.com/questions/135068). – Scortchi - Reinstate Monica Jan 30 '15 at 16:41

1 Answers1

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$I(1)$ model: $y_t=y_{t-1}+\varepsilon_t$

Predictions:

$E(y_{T+1|T})=E(y_{T|T})+E(\varepsilon_T)=y_{T}+0=y_{T}$

$E(y_{T+2|T})=E(y_{T+1|T})+E(\varepsilon_{T+1})=E(y_{T+1|T})+0=y_{T}$

and so on.

[As indicated in the answer here, the more complicated ARIMA(0,1,1) model also has constant forecasts.]

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Glen_b
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