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Im currently developing a simple ARIMA model to forecast a time-series data. Unfortunately my model is not providing good results.

Ive checked if the data is stationary through Augmented Dickey-Fuller Test. Came up as stationary (P< 0,05)

I used auto.arima to verify the p,d,q values, and it provided (2,1,1). Residuals

The dataset has 201 data points and the time-series is measured monthly. I would like to forecast for the next 12 months, although Im still getting very bad accuracy results: 

             ME     RMSE       MAE       MPE     MAPE

Test set 0.06804923 0.348731 0.2659965 -73.86601 140.3297

Why is my MAPE over 100? How can I improve such accuracy, am I missing any step to perform a successful ARIMA model?

DATASET:

structure(c(0.52, 0.36, 0.6, 0.8, 0.21, 0.42, 1.19, 0.65, 0.72, 1.31, 3.02, 2.1, 2.25, 1.57, 1.23, 0.97, 0.61, -0.15, 0.2, 0.34, 0.78, 0.29, 0.34, 0.52, 0.76, 0.61, 0.47, 0.37, 0.51, 0.71, 0.91, 0.69, 0.33, 0.44, 0.69, 0.86, 0.58, 0.59, 0.61, 0.87, 0.49, -0.02, 0.25, 0.17, 0.35, 0.75, 0.55, 0.36, 0.59, 0.41, 0.43, 0.21, 0.1, -0.21, 0.19, 0.05, 0.21, 0.33, 0.31, 0.48, 0.44, 0.44, 0.37, 0.25, 0.28, 0.28, 0.24, 0.47, 0.18, 0.3, 0.38, 0.74, 0.54, 0.49, 0.48, 0.55, 0.79, 0.74, 0.53, 0.28, 0.26, 0.45, 0.36, 0.28, 0.48, 0.55, 0.2, 0.48, 0.47, 0.36, 0.24, 0.15, 0.24, 0.28, 0.41, 0.37, 0.75, 0.78, 0.52, 0.57, 0.43, 0, 0.01, 0.04, 0.45, 0.75, 0.83, 0.63, 0.83, 0.8, 0.79, 0.77, 0.47, 0.15, 0.16, 0.37, 0.53, 0.43, 0.52, 0.5, 0.56, 0.45, 0.21, 0.64, 0.36, 0.08, 0.43, 0.41, 0.57, 0.59, 0.6, 0.79, 0.86, 0.6, 0.47, 0.55, 0.37, 0.26, 0.03, 0.24, 0.35, 0.57, 0.54, 0.92, 0.55, 0.69, 0.92, 0.67, 0.46, 0.4, 0.01, 0.25, 0.57, 0.42, 0.51, 0.78, 1.24, 1.22, 1.32, 0.71, 0.74, 0.79, 0.62, 0.22, 0.54, 0.82, 1.01, 0.96, 1.27, 0.9, 0.43, 0.61, 0.78, 0.35, 0.52, 0.44, 0.08, 0.26, 0.18, 0.3, 0.38, 0.33, 0.25, 0.14, 0.31, -0.23, 0.24, 0.19, 0.16, 0.42, 0.28, 0.44, 0.29, 0.32, 0.09, 0.22, 0.4, 1.26, 0.33, -0.09, 0.48), .Tsp = c(1, 17.6666666666667, 12), class = "ts")

Thanks

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  • $\begingroup$ Can you provide your data, by editing your question and putting the output of dput(your_time_series) in? $\endgroup$
    – Stephan Kolassa
    Nov 29, 2018 at 16:27
  • $\begingroup$ What are the MAPE and RMSE metrics for the test data set with no ARIMA model, just the sample mean? A MAPE of 140 isn't bad by itself, only if, for example, the MAPE of the un-modeled data is, say, 141, in which case the model is not much of an improvement over an ARIMA(0,0,0) model. After all, if you have a process with a mean of 0.001 and a mean absolute deviation of 10, you're going to have a large MAPE even if you know the true mean. $\endgroup$
    – jbowman
    Nov 29, 2018 at 17:29
  • $\begingroup$ There is no improvement between an ARIMA (0,0,0) and any other p,d,q values I set. 0,0,0 - ME RMSE MAE MPE MAPE Test set 0.003380952 0.3100996 0.2432071 99.85578 99.85578 $\endgroup$
    – Guilherme Steffen
    Nov 30, 2018 at 16:57

2 Answers 2

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I took your 201 monthly values and examined them in an automatic mode with AUTOBOX , a time series analysis package that I helped to develop. The model developed is here enter image description here . The Actual,Fit and Forecast graph is here enter image description here and the ACF of the residuals is here enter image description here . The forecast plot for the next 12 periods is here.enter image description here .

There are a number of anomalous data points that will thwart any simple brute force attempt to examine candidate arima structure . auto.arima as it is not robust to latent anomalies (pulses,step shifts, seasonal pulses, local time trends ) and thusly over differences and over paramaterizes arima structure induced by the over differencing.

In terms of your "complaint" about the size of out-of-sample mapes , it all has to do with forecasting "small numbers" as was pointed out by @jbowman .

Finally the plot of the model residuals enter image description here markedly more visually acceptable than yours.

In closing .... to improve the accuracy of any model "Know the Assumptions" as A. Wald wisely reflected.

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I have never seen a time series with negative values where a MAPE would make sense.

I would very much recommend you disregard the MAPE. See What are the shortcomings of the Mean Absolute Percentage Error (MAPE)?. Instead, concentrate on the (R)MSE.

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