Is my time series predictable?

Question

I am new to time series and would appreciate help in this matter.

I have a time series with the following graph as a result of applying the plot_acf in Python. Given this, can it be inferred that this series can be predictable via Machine Learning algorithms? I have already tried LSTM and N-HiTS to predict and the MAE is very large compared to the MAE using a baseline algorithm (the baseline MAE is 20% of the MAE using the previously mentioned algorithms)

I am adding the data that originated this ACF plot, which corresponds to actual sales figures:

324
281
691
281
410
346
86
43
389
43
194
22
0
130
65
173
86
281
0
0
65
43
86
65
0
0
130
65
130
173
151
43
0
43
173
108
173
130
65
0
0
0
86
86
0
22
22
22
22
22
43
43
22
65
130
130
-86
22
173
43
86
43
86
22
65
0
43
43
0
194
0
0
108
108
130
86
86
22
43
86
22
0
0
43
86
22
86
22
0
108
0
65
108
22
86
43
65
43
0
108
86
0
22
65
151
0
43
86
151
43
43
22
108
0
108
0
43
65
43
108
86
0
151
22
0
108
65
65
22
0
43
22
22
65
43
130
151
108
0
130
151
130
65
0
130
43
0
0
22
43
0
65
108
22
65
0
130
86
86
281
216
22
173
108
173
302
410
86
65
65
22
86
22
194
86
130
86
216
108
173
432
238
151
194
194
324
22
367
324
238
367
410
216
497
259
108
281
281
216
108
259
216
130
65
173
86
65
43
43
86
130
194
108
194
238
108
22
43
65
173
86
151
151
130
22
151
86
281
86
259
65
86
173
65
259
173
108
238
130
151
259
259
151
389
65
259
173
238
108
43
65
173
65
65
216
151
302
86
259
130
86
151
65
238
43
86
130
65
130
259
22
432
173
216
108
130
410
324
86
475
130
410
86
216
151
173
85
302
173
259
281
281
86
173
216
302
22
108
43
108
389
245
43
43
216
22
151
302
259
194
346
43
302
194
151
194
173
43
43
281
367
43
367
43
0
65
86
151
108
281
130
22
86
389
324
216
346
43
216
43
130
497
65
22
43
238
324
0
65
43
86
216
238
43
108
194
108
605
302
130
281
86
86
302
173
216
194
86
259
151
389
194
454
65
130
518
216
43
302
22
151
216
65
302
389
281
410
259
238
151
216
389
194
216
130
194
108
65
475
194
216
43
86
86
130
410
324
173
65
86
151
324
475
281
454
130
259
389
216
86
216
194
130
454
194
108
108
43
86
65
238
65
108
86
65
22
108
216
65
65
346
281
86
302
151
324
194
151
151
108
43
0
0
65
324
281
151
0
0
389
302
432
540
108
346
0
194
238
259
130
238
389
238
518
86
281
0
0
108
43
0
0
0
65
0
0
0
0
0
0
108
194
0
216
238
22
43
259
216
22
410
238
86
151
281
259
151
173
432
43
238
65
389
43
173
324
130
367
194
86
65
65
302
367
367
130
216
454
65
0
432
108
0
216
194
108
281
259
108
259
173
238
367
324
259
324
346
346
194
259
151
151
238
65
346
130
562
43
108
173
43
151
65
151
86
43
194
86
22
0
0
65
43
151
43
108
86
0
130
65
65
108
65
22
0
86
0
130
43
108
86
43
108
238
259
324
497
324
346
389
259
324
151
302
389
216
281
216
324
216
194
259
43
108
302
151
22
389
454
194
324
734
0
108
238
22
0
432
108
43
0
22
43
346
43
65
130
86
302
238
475
216
389
281
497
302
65
475
432
259
173
108
216
43
65
173
238
108
86
173
43
173
518
151
281
238
216
151
238
86
173
108
43
108
65
0
259
216
216
22
216
281
259
238
130
86
238
216
173
216
346
648
216
43
302
302
108
259
216
216
194
173
86
194
130
259
194
86
389
65
410

Do you recommend using other methods to determine the predictability of the time series?

Many thanks for the help provided.

You have given us an ACF plot, but neither the original series, nor any information about what the series measures. — Stephan Kolassa, Apr 25 '23 at 20:11
@StephanKolassa thank you for your quick feedback. I have added the information you mentioned. I hope it helps. — 295, Apr 26 '23 at 09:48
Are these daily, weekly, monthly sales, or on some other kind of granularity? Do you only have this single time series, or is this just one of many? — Stephan Kolassa, Apr 26 '23 at 10:31
@StephanKolassa These are daily sales figures, which only happen on weekdays. On weekdays with no sales, zero appears. I only have this time series. If necessary I can try to obtain more datapoints, but this will take quite some effort with associated time. Thank you once again — 295, Apr 26 '23 at 12:03
OK, thanks. Are weekdays for you Monday through Friday, or Monday through Saturday? — Stephan Kolassa, Apr 26 '23 at 13:26
@StephanKolassa Thank you for your answer. I will read the links you provided. In the meanwhile, let me clarify that the low values in the beginning of the series, are due to the COVID period and are clearly understood. — 295, Apr 26 '23 at 15:47
Very good. Then you might be able to improve your forecasts by either removing these data points (i.e., starting the time series later), or using a predictor and running a regression with time series errors. — Stephan Kolassa, Apr 26 '23 at 16:10
In the name of readability, it would be great if you can edit your question to include the data in a more succinct format and at the end of the question. Perhaps something similar to how StephanKolassa included the data in his answer? — dipetkov, Apr 26 '23 at 17:27

score 1 · Answer 1 · answered Apr 26 '23 at 15:13

Your time series does not show any intra-week seasonality (see the seasonplot at the right below). Exponential Smoothing (as per ets() in the forecast package for R) chooses a model with no seasonality, additive errors and an additive trend with strong dampening, so the forecasts are almost flat. Since there is very little time series structure in your data, the prediction intervals are very wide (and actually go below zero, which probably does not make a lot of sense for your data).

Your series does show a number of prolonged periods of low sales. It may be worthwhile figuring out what happened during these times. I believe this has a better chance of improving your forecasts than tweaking the models: How to know that your machine learning problem is hopeless?.

In any case, you have far too little data for a ML method like LSTM to make much of a difference compared to standard time series methods. I recommend the resources here to learn more about forecasting: Resources/books for project on forecasting models

R code:

sales <- c(324L, 281L, 691L, 281L, 410L, 346L, 86L, 43L, 389L, 43L, 194L, 
22L, 0L, 130L, 65L, 173L, 86L, 281L, 0L, 0L, 65L, 43L, 86L, 65L, 
0L, 0L, 130L, 65L, 130L, 173L, 151L, 43L, 0L, 43L, 173L, 108L, 
173L, 130L, 65L, 0L, 0L, 0L, 86L, 86L, 0L, 22L, 22L, 22L, 22L, 
22L, 43L, 43L, 22L, 65L, 130L, 130L, -86L, 22L, 173L, 43L, 86L, 
43L, 86L, 22L, 65L, 0L, 43L, 43L, 0L, 194L, 0L, 0L, 108L, 108L, 
130L, 86L, 86L, 22L, 43L, 86L, 22L, 0L, 0L, 43L, 86L, 22L, 86L, 
22L, 0L, 108L, 0L, 65L, 108L, 22L, 86L, 43L, 65L, 43L, 0L, 108L, 
86L, 0L, 22L, 65L, 151L, 0L, 43L, 86L, 151L, 43L, 43L, 22L, 108L, 
0L, 108L, 0L, 43L, 65L, 43L, 108L, 86L, 0L, 151L, 22L, 0L, 108L, 
65L, 65L, 22L, 0L, 43L, 22L, 22L, 65L, 43L, 130L, 151L, 108L, 
0L, 130L, 151L, 130L, 65L, 0L, 130L, 43L, 0L, 0L, 22L, 43L, 0L, 
65L, 108L, 22L, 65L, 0L, 130L, 86L, 86L, 281L, 216L, 22L, 173L, 
108L, 173L, 302L, 410L, 86L, 65L, 65L, 22L, 86L, 22L, 194L, 86L, 
130L, 86L, 216L, 108L, 173L, 432L, 238L, 151L, 194L, 194L, 324L, 
22L, 367L, 324L, 238L, 367L, 410L, 216L, 497L, 259L, 108L, 281L, 
281L, 216L, 108L, 259L, 216L, 130L, 65L, 173L, 86L, 65L, 43L, 
43L, 86L, 130L, 194L, 108L, 194L, 238L, 108L, 22L, 43L, 65L, 
173L, 86L, 151L, 151L, 130L, 22L, 151L, 86L, 281L, 86L, 259L, 
65L, 86L, 173L, 65L, 259L, 173L, 108L, 238L, 130L, 151L, 259L, 
259L, 151L, 389L, 65L, 259L, 173L, 238L, 108L, 43L, 65L, 173L, 
65L, 65L, 216L, 151L, 302L, 86L, 259L, 130L, 86L, 151L, 65L, 
238L, 43L, 86L, 130L, 65L, 130L, 259L, 22L, 432L, 173L, 216L, 
108L, 130L, 410L, 324L, 86L, 475L, 130L, 410L, 86L, 216L, 151L, 
173L, 85L, 302L, 173L, 259L, 281L, 281L, 86L, 173L, 216L, 302L, 
22L, 108L, 43L, 108L, 389L, 245L, 43L, 43L, 216L, 22L, 151L, 
302L, 259L, 194L, 346L, 43L, 302L, 194L, 151L, 194L, 173L, 43L, 
43L, 281L, 367L, 43L, 367L, 43L, 0L, 65L, 86L, 151L, 108L, 281L, 
130L, 22L, 86L, 389L, 324L, 216L, 346L, 43L, 216L, 43L, 130L, 
497L, 65L, 22L, 43L, 238L, 324L, 0L, 65L, 43L, 86L, 216L, 238L, 
43L, 108L, 194L, 108L, 605L, 302L, 130L, 281L, 86L, 86L, 302L, 
173L, 216L, 194L, 86L, 259L, 151L, 389L, 194L, 454L, 65L, 130L, 
518L, 216L, 43L, 302L, 22L, 151L, 216L, 65L, 302L, 389L, 281L, 
410L, 259L, 238L, 151L, 216L, 389L, 194L, 216L, 130L, 194L, 108L, 
65L, 475L, 194L, 216L, 43L, 86L, 86L, 130L, 410L, 324L, 173L, 
65L, 86L, 151L, 324L, 475L, 281L, 454L, 130L, 259L, 389L, 216L, 
86L, 216L, 194L, 130L, 454L, 194L, 108L, 108L, 43L, 86L, 65L, 
238L, 65L, 108L, 86L, 65L, 22L, 108L, 216L, 65L, 65L, 346L, 281L, 
86L, 302L, 151L, 324L, 194L, 151L, 151L, 108L, 43L, 0L, 0L, 65L, 
324L, 281L, 151L, 0L, 0L, 389L, 302L, 432L, 540L, 108L, 346L, 
0L, 194L, 238L, 259L, 130L, 238L, 389L, 238L, 518L, 86L, 281L, 
0L, 0L, 108L, 43L, 0L, 0L, 0L, 65L, 0L, 0L, 0L, 0L, 0L, 0L, 108L, 
194L, 0L, 216L, 238L, 22L, 43L, 259L, 216L, 22L, 410L, 238L, 
86L, 151L, 281L, 259L, 151L, 173L, 432L, 43L, 238L, 65L, 389L, 
43L, 173L, 324L, 130L, 367L, 194L, 86L, 65L, 65L, 302L, 367L, 
367L, 130L, 216L, 454L, 65L, 0L, 432L, 108L, 0L, 216L, 194L, 
108L, 281L, 259L, 108L, 259L, 173L, 238L, 367L, 324L, 259L, 324L, 
346L, 346L, 194L, 259L, 151L, 151L, 238L, 65L, 346L, 130L, 562L, 
43L, 108L, 173L, 43L, 151L, 65L, 151L, 86L, 43L, 194L, 86L, 22L, 
0L, 0L, 65L, 43L, 151L, 43L, 108L, 86L, 0L, 130L, 65L, 65L, 108L, 
65L, 22L, 0L, 86L, 0L, 130L, 43L, 108L, 86L, 43L, 108L, 238L, 
259L, 324L, 497L, 324L, 346L, 389L, 259L, 324L, 151L, 302L, 389L, 
216L, 281L, 216L, 324L, 216L, 194L, 259L, 43L, 108L, 302L, 151L, 
22L, 389L, 454L, 194L, 324L, 734L, 0L, 108L, 238L, 22L, 0L, 432L, 
108L, 43L, 0L, 22L, 43L, 346L, 43L, 65L, 130L, 86L, 302L, 238L, 
475L, 216L, 389L, 281L, 497L, 302L, 65L, 475L, 432L, 259L, 173L, 
108L, 216L, 43L, 65L, 173L, 238L, 108L, 86L, 173L, 43L, 173L, 
518L, 151L, 281L, 238L, 216L, 151L, 238L, 86L, 173L, 108L, 43L, 
108L, 65L, 0L, 259L, 216L, 216L, 22L, 216L, 281L, 259L, 238L, 
130L, 86L, 238L, 216L, 173L, 216L, 346L, 648L, 216L, 43L, 302L, 
302L, 108L, 259L, 216L, 216L, 194L, 173L, 86L, 194L, 130L, 259L, 
194L, 86L, 389L, 65L, 410L)
sales_ts <- ts(sales,frequency=5)
library(forecast)
par(mfrow=c(1,2),las=1)
model <- ets(sales_ts)
plot(forecast(model,h=20))
seasonplot(ts(sales,frequency=5),pch=19)

Is my time series predictable?

1 Answers1