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I am working on a forecasting problem, where i am planning to forecast the value for the current time step (real value 43 in data below in a[4] column). The data is in the form of values at each timesteps. Sample data is as follows:

| steps         | a[1] | a[2] | a[3] | a[4] |
|---------------|------|------|------|------|
| latest_step-6 | 67   | 79   | 85   | 87   |
| latest_step-5 | 78   | 71   | 79   | 81   |
| latest_step-4 | 54   | 59   | 69   | 74   |
| latest_step-3 | 34   | 40   | 46   | 48   |
| latest_step-2 |      | 51   | 56   | 65   |
| latest_step-1 |      |      | 65   | 71   |
| latest_step   |      |      |      | 43   |

The above table describes the values of a variable "a" (a[1], a[2], a[3] etc. all point to same variable a). The different columns represent the updated values of the variable "a" as new data comes at the latest time steps. (Bascially the latest data may or may not change the older timestep values, i.e. the values corresponding to -1, -2 lags etc.). To put in perspective how the data may change with each new time steps, the snapshot of above data, when the latest data didn't come is as follows:

| steps         | a[1] | a[2] | a[3] |
|---------------|------|------|------|
| latest_step-5 | 67   | 79   | 85   |
| latest_step-4 | 78   | 71   | 79   |
| latest_step-3 | 54   | 59   | 69   |
| latest_step-2 | 34   | 40   | 46   |
| latest_step-1 |      | 51   | 56   |
| latest_step   |      |      | 65   |

I am looking for some papers, references, methods, algorithms to determine the latest_step value (43 in above examples) using not just a[4] (can use univariate time series methods for that) but all the other values too (a[1], a[2] etc.) as they may/may not (if not then why?) contribute to what the latest time step value may come up at a[4]. Any help in this regards would be appreciated.

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  • $\begingroup$ Kalman filter may be what you're looking for. $\endgroup$
    – mloning
    Commented Jun 3, 2020 at 7:57
  • $\begingroup$ Can you be a little more specific. Highly appreciated. Any links or info, how kalman filter applies here would help. $\endgroup$
    – Mr. Confused
    Commented Jun 3, 2020 at 7:59
  • $\begingroup$ The general setting is dynamic online learning.. There are various tutorials online on Kalman filtering ( (e.g. cs.unc.edu/~tracker/media/pdf/SIGGRAPH2001_CoursePack_08.pdf). $\endgroup$
    – mloning
    Commented Jun 5, 2020 at 9:07

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