ARIMA

Using ARIMA Models on Google Search Data

Predicting time-series data can be challenging depending on the priors. Here we are going to look at two cases, both using ARIMA models to see how predictions are affected.

ARIMA on non-periodic data

We begin by importing important packages such as numpy and pandas. We'll analyze data found here.
Note that the data has already been downloaded locally and renamed as 'data.csv'.

	Date	Open	High	Low	Last	Close	Total Trade Quantity	Turnover (Lacs)
0	2018-10-08	208.00	222.25	206.85	216.00	215.15	4642146.0	10062.83
1	2018-10-05	217.00	218.60	205.90	210.25	209.20	3519515.0	7407.06
2	2018-10-04	223.50	227.80	216.15	217.25	218.20	1728786.0	3815.79
3	2018-10-03	230.00	237.50	225.75	226.45	227.60	1708590.0	3960.27
4	2018-10-01	234.55	234.60	221.05	230.30	230.90	1534749.0	3486.05

Now that we see what the data looks like, we need to reformat the data slightly. As is common with time-series data, we first convert the index into dates using to_datetime().

Finally, we'll plot the Close prices for each datapoint.

Now it's time to train the ARIMA model! pmdarima (formerly pyramid is based on statsmodels and offers more functionality for training ARIMA models.

We now see that the forecast is quite poor. However, because the data does not show an obvious periodic trend, a horizontal line is a better prediction than other predictions you might expect.
Let's see next what happens when we use ARIMA on a dataset with more periodic trends.

ARIMA on Periodic Data

Now that we've seen how an ARIMA model (doesn't) work on data with weird trends, let's see how it performs given data that we know to be periodic.

I did a quick search for christmas in the US on Google Trends and downloaded the data for the past 16 years.

Let's load that in and see what it plots!

So we see that the data is periodic with no obvious trend over time. Let's see what our ARIMA model does now!

From this we can see that our model did a great job at predicting what happens on a 12 month cycle. However, it failed to predict any changes in peak search count over time. That's one of the shortcomings of ARIMA models. While they can be powerful tools to find periodic trends, they work less well at capturing subtle trends (though, most models would struggle with this particular data).