# Chosing the right time series model

Can someone help me to find the right time series model. I am not able to figure out the right hyper parameters for the model. Please see attached ACF and PACF graphs. I can provide more information if someone is willing to help.

I am using monthly data from 2013 to august 2019

• Have you tried an automated model selection method, like ets() or auto.arima() in the forecast package for R? If not, why is manual model selection important to you? – S. Kolassa - Reinstate Monica Nov 6 at 9:22
• Please find the uploaded csv. link - In the above example I was trying to forecast compact category. Yes, I have tried using Auto.Arima and ets in alteryx (R package) – Spun Nov 6 at 17:16
• you have 6 series each with 81 monthly values. The appropriate model for each series is likely to be similar with subtle differences between then . Pick one series ...the one that you are having the most trouble with and I will analyze that .. pursuing a potential hybrid model using both memory (arima) and latent deterministic structure. Please select one. – IrishStat Nov 6 at 20:09
• @ IrishStat , Thank you for your reply again sir. I think my pick would be Compact. I would love to understand the methodology and the thought process. Looking forward – Spun Nov 7 at 17:04
• I will try to accomplish that ... my post might be quite long as modelling is an iterative process much like peel an onion. – IrishStat Nov 7 at 20:55

There is nothing wrong whatsoever in using computerized aids as long as you understand the strengths and the shortcomings. Building a model is much like washing both sides of your face .. one needs to deal with both potential auto-projective (memory/arima) structure and deterministic structure ( pulses, level shifts , seasonal pulses and local time trends ). The approaches you have been investigating only deal with memory and are often flawed with over-parameterization and resultant statistical non-significance.

I have looked at your 7 series and perhaps the least complicated/thorough model formulation is the one you selected ...compact car sales over 81 periods . For pedagogical reasons I would have selected a more "difficult" series but life is short and I have analyzed the one you selected.

I will present the results of AUTOBOX's ( a piece of software that I have helped to develop ) and show critical results ...and then in a second phase actually try and unveil the logic behind the steps.

Initially the acf of the original series is here clearly suggesting strong seasonal auto-regressive structure akin to the classic airline series of Box and Jenkins. The suggested model is (2,0,0)(1,0,0) a quite simple model in thew span of possibilities. I can't imagine why even band-limited procedures wouldn't deliver a similar model because the identified anomalies are VERY small BUT highly significant.

The Iterative modelling process https://autobox.com/pdfs/ARIMA%20FLOW%20CHART.pdf evolved to the following potentially useful model .

and here in more detail withmodel statistics here

The Actual/Fit and Forecast is here with monte-carlo driven re-sampling prediction limits for the next 36 periods .

The model residuals are here with an ACF here

The forecasts are here

The Actual and Cleansed graph is helpful to visually sipport the identification of the anomolous data points

I will now take a deep breath and attempt to detail the steps as you indicated that is what you really want.

STEP 1 : examine possible models following two mutually exclusive and distinctive paths ... Path 1 .. investigate possible arima models using a superset of the aic/bic ... auto.arima approach and for each possible prospect identify and incorporate additional deterministic structure that is statistically significant THEN take Path2 which identified deterministic structure and then incorporates/adds any evidented arima structure..... Select the most promising path penalizing models for excessive parameters

Note that models of the form are also considered as a wide search is made for an equation that is as good as the human eye or at least similar as possible.

In this case the best model had an a seasonal ar(12) and a 2 parameter ar polynomial

STEP 2 possible deterministic structure via the Tsay procedure http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html

Continuing we test for constancy of error variance over time .. suggesting constant error variance over time ( one of the Gaussian assumptions ignored by others ! ) Note that some of your other automotive series series required this GLS OPTION .

We now more closely examine the need for just pulses ....and obtain

stepping down ( always a good idea ! ) we get

In terms of why your current approaches are failing , I can only suggest that you closely read @Adamo's wise reflections

"The correlogram should be calculated from residuals using a model that controls for intervention administration, otherwise the intervention effects are taken to be Gaussian noise, underestimating the actual autoregressive effect."