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ARIMA: Why it is Important in Modeling of Financial Time Series

Writer's picture: Tian Khean NgTian Khean Ng

ARIMA stands for Autoregressive Integrated Moving Average. It is a technique used by Economists to forecast economic time series, which have some common characteristics with financial markets data. For example, current values are related to past values (in the sense of past values having an impact on current values), and each day previous to the current day is 1 lag. The impact of the lag diminishes the further away they are from the current day. ARIMA can also be used for economic time series that are seasonal such as the demand for Natural Gas or electricity for heating in the Winter months.


But the main reason why ARIMA is important in modeling financial times series is that using it we can glean insights from the data to build our models with more sophisticated technologies such as Artificial Intelligence. In the paragraphs below we explain the various concepts used in ARIMA.


The ACF (Autocorrelation Function) Chart

Autocorrelation as we have explained in the introduction to this article is the ‘memory’ of the time series. Past values affect the current value.


Below, we see that for this ETF, the memory of its past price  lasts approximately 10 days gradually losing its impact after which it falls below the Red 95% Confidence Level line. There a Moving Average of 10 days is suitable for analyzing this ETF.



The PACF (Partial Autocorrelation Function) Chart

The PACF measures the correlation between the time series and its lagged values while controlling for the correlations at shorter lags. It helps to isolate the direct effect of a particular lag. The sharp cut-off after lag 2 suggest that the autocorrelation effect peters out after 2 lags (2 days) 



 

Differencing a time series

A time series can be differenced to get rid of trends, to stabilize the Mean, and to make it stationary, by subtracting the current value from the previous value. Thus, the price chart of an ETF would look like this when differenced by 1 lag.



 

Putting it all together

When you initiate an ARIMA, you have to specify your values for the following parameters:

p is the autoregressive parameter. In our PACF chart above we saw that p is of the order of 2

d is the differencing. Usually, as we have seen in the chart above, d=1 will do but sometimes for really non-stationary time series, d can be 2.

q is the Moving Average parameter; our chart shows that q is about 10. But in the case of financial times series, q=5 is commonly used because 5 days is the trading week.


The Fitted ARIMA and forecasting

The chart below shows the time series and its fitted values (Red dotted line) after an ARIMA of p=2, d=1 and q=5 was applied.  ARIMA can also do a forecast, In the chart below you can see that it has forecasted for 5 days ahead (Red dotted line).

But it is too simple and not reliable for equities and other financial time series. Therefore our models have several stages and ARIMA is used in the earlier stages to pre-process the data.



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