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I want to perform an analysis on timeseries data which is measured per second.

To give some context, it is a data of temperature of air at the exit of air heater. Fluctuations in data are either due to switching on and off around setpoint or partial switching of (1 of 2 coils) heater. Sustained low temperatures observed are due to heater being switched-off for considerable amount of time.

Sample data of temperature is as represented in following images:-

enter image description here enter image description here

As per my understanding, prediction of any such data at particular time instant depends on past observations as well as on other factors (e.g. power to heater, mass flow rate of air etc.).

Most of timeseries analysis examples that I read on web were for data with higher timeperiod per observations (week, month, year). These gives to my mind some questions:-

  1. Is timeseries analysis a suitable method for prediction of my Temperature data? If not then why?
  2. If no to first question, then what predictive method can be used for such data (apart from first principle modeling)?
  3. How can the effect of certain background parameters (e.g. Mass flow rate of air, heater power) that are fixed during one observed series be included in overall analysis. For e.g. a certain Temperature profile is observed for 10,000 seconds for 1,000 W heater and 200 CFM and another profile for 10,000 seconds for 1,200 W heater and 220 CFM. Now each series can be analyzed on it own (maybe?). But how to include effect of start parameter (e.g. heater power) on from scratch prediction of new series?
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  • 2
    $\begingroup$ Your time series is heavily driven by causal factors. The very first thing you need to do is forecast when people will switch the heater on or off. (Unless you only want to forecast one second ahead, in which case a naive forecast - just project the last observation forward - will probably be best.) $\endgroup$ – S. Kolassa - Reinstate Monica Mar 14 '18 at 16:43
  • $\begingroup$ I'm voting to leave this open, a bit of copy editing for clarity. @StephanKolassa's comments are very good and could/should be addressed. A model to consider would be a Kalman Filter, as they're very good at estimating control systems (e.g. timeseries which are heavily driven by causal factors). They are essentially the same, the latter is more specific. $\endgroup$ – AdamO Mar 15 '18 at 16:29
  • $\begingroup$ if rules for discrete event are known aforehand (for e.g. Heater switched off at cutoff Temperature and not turned on till lower threshold, both of which are known.), then would the Kalman Filter be applicable? $\endgroup$ – user1768201 Mar 15 '18 at 18:42
  • $\begingroup$ I think the closest time series model would be en.wikipedia.org/wiki/SETAR_(model) Kalman Filter are very flexible but Markov switching statespace model will be difficult because of the endogenous switching in this case. $\endgroup$ – Josef Mar 16 '18 at 14:42
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As per my understanding, you can perform time series analysis even on short time period observations.

You can use ARIMA model which is available in both Python and R for modelling time-series and predicting future data.

So, to answer your questions,

Ans.1 : Yes, time-series analysis is suitable for this data as well.

Ans.2 : I'll answer this question from Python perspective. ARIMA model is available in python, but there no in-built function to decide best fit ARIMA model (Which is available in R). So, you need to plot graphs from your data. You'll need to plot auto-correlation plots like ACF (Auto Correlation Function) and PACF (Partial ACF), which shows the correlation between observations of a time series separated by k time units (lags). Means after how much time the pattern is repeated. So, based on ACF and PACF plots, you can decide parameters(p,d and q) of ARIMA model (From PACF plot decide q and from ACF plot decide q). I find this post very helpful to learn about ARIMA.

Sorry, I don't have any idea about last question.

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