What are the best practices for ensuring accuracy and reliability in multivariate time series analysis?

Throughout my teaching and practical model-building experience, the age-old adage "one size doesn't fit all" remains ever relevant. For instance, I've witnessed projects where a simple model outperformed a complex one because it was better suited to the nature and volume of the data. Continual learning is essential. As newer methods emerge, they might offer advantages over traditional ones. For instance, advancements in deep learning have led to architectures like LSTM or GRU that have shown promise in multivariate time series forecasting. Remember, each technique is just a tool; understanding when and how to wield them is the key to effective analysis.

The choice of method should not just be about the data at hand but also about the end goal of the analysis. For instance, if you're looking at financial markets, a GARCH model might be more suitable due to its ability to model volatility. However, for economic data analysis, a VAR or VEC model might be more appropriate. The key is to not get swayed by the complexity or popularity of a method but to choose one that aligns best with your data characteristics and analysis objectives.

I will try to generalize the answer: As per my experience first thing is Data Understanding & and building assumptions to fit the right conclusion before fitting the right model. Then comes Feature Engineering which itself has much more importance while building any conclusion, analysis, or building model. The better you understand your end goal & and dataset ,it's a one step closer to the right solution.

Data preprocessing is often underemphasized, yet it's the backbone of any reliable analysis. Especially in time series, overlooking aspects like seasonality or ignoring non-stationarity can lead to misleading conclusions. Also, preprocessing isn't just a technical step; it's where you start understanding the story your data tells. For instance, the pattern of missing values can itself provide insights into the data generation process.

Missing values are particularly important in time series analysis. Differencing a series once turns one missing value into two. A similar thing can be said about lagging values and errors. Both missing values (and outlier values) can be imputed. Much of the other content under this heading I wouldn't consider preprocessing data. For instance, testing for stationarity is not preprocessing data. However, these tests may motivate further processing. This section exaggerates the impact of non-normality. Non normal variables can be transformed into normal ones. Non-normal errors can be addressed by more fully specifying the model. A state-space/GARCH model is not the correct response. A GARCH model is used to model volatility.

Model validation is where theory meets reality. It's not just about statistical measures but also about the model's practical relevance. For instance, a model with great AIC/BIC scores but poor performance in real-world scenarios is of limited use. Also, cross-validation techniques, particularly in time series, need to be carefully designed to avoid look-ahead bias.

Cross validation via walk forward optimization through expanding or rolling windows helps in visualizing the efficacy of the general structure in the model.

This is the correct point where you test errors for normality, stationarity, heteroskedasticity, and serial correlation. You can also test the coefficients of the model for statistical significance and expected sign. Otherwise you can focus on forecasts and prediction error in backtesting.

Beyond Coefficients: It's about storytelling. What do these coefficients mean in the real world? For instance, in economics, a coefficient isn't just a number; it's about understanding economic behaviors and policies. Contextualizing Results: How do these results fit into the larger body of knowledge? Are they challenging existing theories or reinforcing them?