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basically this is the first time I applied TS analysis to a real dataset. ACF and PACF plots are not as nice as in hypothetical settings. I need help interpreting the results.

I am analysing sales data with clear 7 days and 30 days seasonality.

TS is non-stationary by the Augmented Dickey-Fuller (ADF) test.

First-order differencing removes non-stationary by Augmented Dickey-Fuller (ADF) test. (p-value ~ e-10)

However, my ACF and PACF plots for First-order differenced TS show a clear seasonal trend.

lag=40: ACF: https://ibb.co/B66wSCm PACF: https://ibb.co/dMbty3W

lag=100: (ACF is still v. significant after lag=100) ACF: https://ibb.co/xYVxzvJ PACF: https://ibb.co/1ZHKxP7

more interestingly, when I apply 7th-order differencing, I got this: ACF: https://ibb.co/4g2SwM2 PACF: https://ibb.co/mzmV5Nn

I get for seasonal components in TS, the SARIMA model is more suitable. I wanted to manually find p and q based on ACF and PACF. for more analysis (plots and context), here's my code: https://www.kaggle.com/code/bigsmallmediumpotato/time-series-analysis-store-sales

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  • $\begingroup$ (1) I do not quite see a 30 day seasonality in your data. But if there is one, then SARIMA may not be quite the best tool. There are special methods for time series with multiple seasonalities. (2) The (P)ACF is only of limited use, because it can only be used to determine "pure" AR or MA models. The gold standard is still a search over possible models and minimizing information criteria, as per the forecast and fable packages for R. $\endgroup$
    – Stephan Kolassa
    Commented Sep 30 at 21:34
  • $\begingroup$ Please clarify your specific problem or provide additional details to highlight exactly what you need. As it's currently written, it's hard to tell exactly what you're asking. $\endgroup$
    – Community Bot
    Commented Sep 30 at 23:13
  • $\begingroup$ Thanks @StephanKolassa , I get I can't use p or q values from ACF and PACF which are designed for AR, MA or ARMA processes. I plan to implement a gird search to find the best params for SARIMA. (I will implement SARIMA first then look at other models maybe.) Separate question: Is time series analysis only good for analysing seasonal trends?? Suppose I get access to real-time market data, e.g. stock prices and index, how would you approach analysing a series using TS analysis? $\endgroup$
    – username_1326
    Commented Oct 1 at 17:31
  • $\begingroup$ Question: for time series data with no clear seasonal trend, e.g. stock prices or index, can you still use Time Series for forecast? what are its limitations? So I guess GARCH is a good starting point, but where can I go after that. $\endgroup$
    – username_1326
    Commented Oct 1 at 20:07
  • $\begingroup$ I'm not quite sure I understand what you mean by "time series analysis". Analyzing time series for forecasting (there are also other use cases, like anomaly detection, or time series clustering etc.) is a vast field. Would you consider fitting a state space or ETS model "time series analysis"? Or are you mainly thinking about only ARIMA methodology? You can absolutely analyze nonseasonal time series for forecasting, among them market returns (where the EMH implies that forecasting will be hard), using GARCH or other. $\endgroup$
    – Stephan Kolassa
    Commented Oct 1 at 20:46

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