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I am interested in getting a better sense as to when to use time series techniques.

Let's say you have a data set with units sold as the response. Your goal is to predict units sold on any given day. If you were to plot units sold against time, let's say you see an obvious increasing trend and seasonality.

When would it be better to use a time series technique vs. just building a regression tree and hope it splits on features like (day count, month, year, day, etc...)?

On the one hand, it makes sense that tomorrow's sales will be closer to today's sales than it would be to sales 10 year ago. This would suggest a time series model.

But on the other hand, realistically, there is little economic rationale stating that tomorrow's sale's depends on today's sales. Wouldn't using a tree be more useful as basically you are dividing time into a lot of thresholds. For example, if we are in 2020 as opposed to 2010, predict a higher average sale. If we are in summer as opposed to winter, predict a higher average sale. To capture the overall increasing trend, we can include day count as a feature, and thus higher day counts lead to higher sales.

So when we want to use a time series model?

Thanks!

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I don't know if there is a rule of thumb or not. You use time series regression for several reasons. One is when autocorrelation is indicated (there are many tests to determine if it is). Or when you think that X influences Y now (t(0), and at points in the future t(1), t(2)...). Or when the impact of X on Y changes over time. Note that slopes and R squared values will be distorted (they will be higher) when you are measuring the relationship of two variables with each other over time unless there is cointegration (this may be a problem even with cointegration which in any case requires a specific form of time series).

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" tomorrow's NEW sale's depends on today's sales " is never the conclusion because that is naive and clearly false as the past never causes the future . What you do today may be correlated with what you did yesterday BUT yesterday is not the cause.

Last month's sales do not cause this month's sales but last month's sales may have been caused by the # of salesman and if the # of salesman remains constant or the pattern of the history of salesman remains constant then previous sales can be a barometer of this month's sales BUT it is never the cause just a proxy for what you didn't specify.

What is said is that given what factors are causing sales is constant then previous sales are a PROXY for the the unspecified causal factors.

This is why modern time series analysis uses a possible triad of factors ...

1) causal variables and their lags (X)

2) unspecified stochastic causals whose effects are being proxied by lags of the series being forecasted (arima component). Note that arima models using error terms are equivalent to memory models in Y .

3) latent deterministic structure(I) such as level shifts , local time trends , seasonal pulses and pulses ALL of which are proxies for unknown deterministic effects AND should be investigated/detailed to uncover the true cause.

See http://www.autobox.com/pdfs/regvsbox-old.pdf for a discussion of arima and regression with time series data (transfer functions or SARMAX) . See https://autobox.com/pdfs/SARMAX.pdf for a presentation of the the three kinds of factors

As usual the role of a good moderator is always to tease out more and more and more ... so here goes with some more .. I hope this helps just a little bit

if y(t)=3+2*x(t) + a(t)

true state of nature BUT we only have the past of y and we don't know x

if x(t)=[theta(B)/phi(B)]*e(t)

then by substitution

   y(t)=3+2*{[ thetha(B)/phi(B) ]*e(t) } + a(t)

   y(t)= is then a combination of e(t) and a(t) culminating

   y(t)=[ma/ar]*w(t)

an arima model is a poor man's regression model .

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    $\begingroup$ If "the past never causes the future," then what does? (I do understand what you mean in the sense of "the data we are using about the past are insufficient to predict the future with complete accuracy," but I found your assertion to be quite amusing.) I see no answer in your post to the question, "so when [do] we want to use a time series model?" $\endgroup$ – whuber Feb 14 at 22:43
  • $\begingroup$ if you refer to a "time series model " as a pure memory model without causals (as you may not know them or can't suggest them) "the past is prologue" as it is all that you have to go on. $\endgroup$ – IrishStat Feb 14 at 22:50

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