How do you deal with seasonality and trends in mfts with missing data?

One effective approach to handling missing data is imputation, where missing values are filled in with reasonable estimates. Imputation can help maintain the seasonality and trend components of the data, preserving valuable information and reducing bias. However, it’s important to recognize that imputation is not a flawless solution; it can introduce uncertainty and potential errors into the dataset, impacting the statistical properties of the time series. Therefore, selecting an appropriate imputation method that aligns with your data characteristics and analysis objectives is crucial for ensuring the reliability of your results.

To address seasonality and trends in multivariate time series (MFTS) with missing data: Imputation: Use techniques like interpolation, forward/backward filling, or advanced methods like KNN, MICE, or deep learning-based imputation to fill missing values. Decomposition: Apply methods like STL (Seasonal-Trend decomposition using LOESS) to separate seasonal and trend components. Modeling: Use models that handle seasonality and trends, such as ARIMA with seasonal components (SARIMA) or exponential smoothing (Holt-Winters). Advanced Models: Consider machine learning models like LSTMs or Prophet that can handle complex patterns and missing data.

In my experience, dealing with seasonality and trends in time series data with missing values can be challenging. One technique I have found useful is to decompose the time series into trend, seasonal, and residual components. By modeling each part separately, the impact of the missing values can sometimes be isolated and handled more effectively. For example, I will often fit smooth trend and seasonal curves to the available data, ignoring gaps. Then I examine the residuals - the leftover variation after removing trend and seasonal patterns. If the residuals appear noisy or random, it model has accounted for structural patterns despite missing observations. If residuals show clear new patterns, it indicates initial model was inadequate.

To handle seasonality and trends in multivariate time series (MFTS) with missing data, start by imputing missing values using methods like interpolation. Then, decompose the series into seasonal, trend, and residual components using techniques like STL. This allows you to analyze and model each component separately. After processing, reconstruct the complete series by combining the components, ensuring more accurate forecasts and insights despite the missing data.

When forecasting store sales, I noticed unusual gaps in the historical data. However, my colleague shared that there had been supply chain issues that temporarily affected inventory levels during those periods. Knowing this context allowed me to better account for the missing observations rather than solely relying on quantitative methods. In general, I've found it very valuable to collaborate with subject matter experts when analyzing complex time series. By combining quantitative rigor with qualitative insights, more reliable and interpretable models can be built even with imperfect data. A human-machine team often outperforms either alone.

Seasonal Moving Averages: Calculate seasonal moving averages using a window of suitable size (e.g., the same period in the previous years). Impute missing values using the corresponding moving averages. Multiple Imputation: If your data has complex interactions and dependencies, consider using multiple imputations. This involves creating multiple imputed datasets by simulating plausible values for missing data based on the observed data's distribution and relationships.