Using Auxiliary Series and Recursive Forecasts in Time-Series Models

Summary

The document raises practical questions about forecasting one financial series with information from another, using Microsoft and the S&P 500 ETF as an example. It considers jointly modeling both series as a vector time series, and asks how auxiliary information can be incorporated into a forecast. It also asks whether an autoregressive model should be applied recursively, feeding its first predicted value into the next forecast step.

A further question concerns numerical forecasting methods framed as optimization problems rather than relying heavily on statistical distribution assumptions. The document offers no answers, model comparisons, empirical results, or recommended techniques. It is therefore best read as a set of research questions about multivariate forecasting, multi-step prediction, and distribution-light methods, rather than as evidence for a particular strategy. The suitability of any approach would depend on the data, forecast horizon, and validation procedure.

Key ideas

• Auxiliary series such as a market index may provide information for forecasting an individual equity series.
• Joint vector time-series models are one possible way to represent relationships among multiple series.
• The document asks whether autoregressive forecasts should be iterated using earlier predicted values.
• It seeks forecasting methods based on numerical optimization with fewer distributional assumptions.
• No answers or empirical comparisons are provided.

Tags

# Forecasting time series data using auxiliary information and associated questions


# Forecasting time series data using auxiliary information and associated questions












Suppose I want to forecast MSFT time series, using MSFT history as well as SPY history. Are there good time series forecasting methods that permit auxiliary data to be used? Perhaps you should just model the entire time series (MSFT and SPY jointly) as a single vector time series?

Also, suppose we impose an autoregressive model (with lag $h$) $$ \hat x_{t+1} = f(x_{t-h + 1}, \dots, x_t) := \theta_1 x_{t} + \cdots + \theta_{h} x_{t- h +1} + v. $$ Why not predict $\hat x_{t + 2} = f(x_{t-h+2}, \dots, x_{t}, \hat{x}_{t+1})$? It seems that most predictive models don't do this for some reason or another.

Also, I'm wondering if there are good explanations of numerical methods to forecast time series that don't rely so much on statistics. Not that I don't understand statistics, but I prefer distribution-free assumptions and weaker assumptions on the underlying structure (similar to how least squares can be thought of as an MLE estimate or as the solution to the squared-error minimization problem).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.