I am having a small project on Time series analysis for that I have hourly sales data for that I need to forecast hourly sales for the next 1 month, i.e around next 720 hours I am exploring ARIMA for building models below are few doubts I got when I am exploring ARIMA Any help with clear explanations is highly appreciated

  1. In ARIMA How order parameters are different from seasonal parameters based on my understanding order parameters P, D, Q is AR,I, MA components which are AR is how many previous lags needed in predicting next value(we can see PAC graph for identifying this component at what lag the immediate downfall is happening in partial autocorrelation) plz correct me if I am wrong
  2. "I" component is Differencing component to bring the series into Stationarity (here I have doubt stationarity means mean,variance and autocorrelations are constant over a period of time what I read in many times but not clear about what that period of time means is that like checking all components for hourly/weekly/biweekly/monthly/quarterly/yearly (as my data in hourly volumes)
  3. MA components how may previous error components should i used for forecasting next value(we can use ACF plot to identify this component based on immediate downfall of correlation of diff lags in ACF plot if the correlation is falling with lags very slowly in my understanding we need to differentiate the data to bring the stationarity and then we have to check at what lag quick fall in correlation to use as MA component (plz correct me if I am wrong)
  4. The seasonal component also have same parameters as order component but I am unable to distinguish these from order parameters AR, I, MA and explain the difference and how to identify these optimal parameters
  5. and I have differenced the data once and checked for stationarity using Dickey-Fuller test(adf.test in R) it is saying data is stationary with P<.05 but when I check the same with "kpss.test" it is saying data is nonstationary with P>.05 could you plz explain why
  6. also please explain if I have hourly data how to check seasonality because data become huge as data is in hourly volumes(do I have to plot data hourly/weekly/biweekly/monthly/quarterly/yearly to check seasonality )
  7. also, can I create a data frame using last 24 lags as 24 columns and pass to crime as covariates(XREG component) to model the ARIMA Errors(for hourly data or 7 lags for daily data) will it helps
  • $\begingroup$ Great project! You might be better off splitting your 7 questions into several questions. Also you might be better off with another model, e.g. tbats instead of ARIMA. $\endgroup$ – Ferdi Aug 27 '18 at 13:33

If you have hourly data and you wish to forecast the next 30 days then you should consider incorporating 1) hour-of-the-day , 2) day-of-the-week , 3) week-of-the-month , 4) week/month of the year . 5) pre ,contemporary and lag effects of known events/holidays , 6) long-weekend effects , 7) day-of-the-month , 8) arima and sarima memory effects , 9) unspecified pulse,level shifts,seasonal pulses,local time trends , 10) any user-specified causal series.

This problem/opportunity arises normally, for example see call-center forecasting e.g. http://demand-planning.com/2010/03/18/can-forecasting-help-me-staff-a-specific-hewlett-packard-call-center-at-1030-am-on-a-friday/

Your final model should incorporate both exogenous effects as well as possoble endogenous effects (arima). Leaning just on the rear-window i.e. arima is nearly always inadequate when you can identify deterministic structure. Memory (arima) structure is a proxy for variables that you have not identified or included .

I have not answered your detailed questions as they are purely memory based (endogenous) questions which is not my preferred mode. Perhaps the sheer number of questions that you are having is a clue for you to expand your analytical horizons.

For a literature review you might start here https://stats.stackexchange.com/search?q=user%3A3382+HOURLY+DATA

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