Abstract: Missing data presents a significant challenge when forecasting unknown data in time series. To address this issue, this paper proposes an Attenuated Long and Short-Term Memory model based on a decaying function, which is abbreviated as AD-LSTM, for forecasting unknown data in time series. As strong correlations exist in adjacent data, the Grey model is leveraged to predict and impute missing values in small-sample datasets. To improve the accuracy of forecasting in time series with missing data, we introduce subspace decomposition, which can correct errors in the memory state cell caused by missing elements, and a time decay function, which utilizes the number of adjacent continuous missing data as a weight to modify the memory cell and enables the model to detect the existence of missing elements, into the LSTM unit. These enhancements reduce the impact of imputed data on model training in time series analysis. Finally, to verify the effectiveness of our proposed method, we conduct experimental validation and comparative analysis using the Beijing house price dataset. Our results indicate that the AD-LSTM model performs better in reducing the impact of missing data and achieving lower forecast errors compared to the baseline models.  

Key words: Forecasting Model, Grey Model, Decaying Function, Subspace Decomposition