I apologize for the incomplete response. It seems there was an error when trying to import the 'arch' module, which is required for the ARIMA-GARCH model. Let me provide a detailed explanation of the methods we were able to implement successfully, along with their results and visualizations.
- Hidden Markov Model (HMM)
The Hidden Markov Model is a statistical model that assumes the system being modeled is a Markov process with unobserved (hidden) states. In our case, these hidden states represent bull and bear markets.
Results:
- The HMM identified two distinct market regimes in the
cad_ig_er_index
. - The plot shows the index value over time, with shaded regions indicating bull and bear markets as identified by the HMM.
- This method captures the idea that market regimes have different underlying dynamics, which can persist over time.
- Gaussian Mixture Model (GMM)
The Gaussian Mixture Model is a probabilistic model that assumes all the data points are generated from a mixture of a finite number of Gaussian distributions with unknown parameters. In our application, we use it to cluster the returns into two regimes.
Results:
- The GMM also identified two market regimes in the
cad_ig_er_index
. - The plot shows the index value over time, with shaded regions indicating bull and bear markets as identified by the GMM.
- This method allows for more flexible modeling of the return distributions in each regime.
- Change Point Detection
Change point detection algorithms aim to identify points in time when the statistical properties of a sequence of observations change. We used the Pruned Exact Linear Time (PELT) algorithm for this purpose.
Results:
- The plot shows the
cad_ig_er_index
over time, with vertical red dashed lines indicating detected change points. - These change points represent significant shifts in the statistical properties of the index, which could indicate transitions between bull and bear markets or other regime changes.
- Random Forest Classifier
Random Forest is an ensemble learning method that constructs multiple decision trees and merges them to get a more accurate and stable prediction. We used it to classify market states based on various features.
Results:
- Classification Report: This shows the precision, recall, and F1-score for both bear and bull market predictions.
- Feature Importance Plot: This bar chart shows which features (economic indicators) were most important in classifying bull and bear markets.
- Long Short-Term Memory (LSTM) Network
LSTM is a type of recurrent neural network capable of learning long-term dependencies in sequence data. We used it to predict market states based on sequences of past returns.
Results:
- Classification Report: This shows the precision, recall, and F1-score for both bear and bull market predictions using the LSTM model.
- Training and Validation Accuracy Plot: This shows how the model's accuracy improved over training epochs, for both the training and validation datasets.
- Wavelet Transform Analysis
Wavelet transform decomposes a signal into different frequency components, allowing us to analyze both time and frequency information simultaneously.
Results:
- The plot shows the wavelet decomposition of the
cad_ig_er_index
at different levels. - Each level represents different frequency components of the index, potentially revealing patterns at various time scales.
Statistics for HMM and GMM models:
For both the HMM and GMM models, we calculated the following statistics for each identified market regime:
- Average Return
- Standard Deviation
- Sharpe Ratio
- Percentage of Time in each market state
These statistics provide insights into the characteristics of bull and bear markets as identified by each model, including their relative performance and risk.
Conclusion
Each of these methods offers a different perspective on identifying and characterizing bull and bear markets in the cad_ig_er_index
. The HMM and GMM provide direct classifications of market states, while change point detection identifies significant shifts that could indicate regime changes. The Random Forest and LSTM models offer predictive capabilities based on various features and historical patterns, respectively. Finally, the wavelet transform analysis allows for a multi-scale examination of the index's behavior.
By combining these approaches, we get a comprehensive view of how the cad_ig_er_index
performed in different market regimes, the factors that influence these regimes, and how they can be identified and potentially predicted.
Would you like me to elaborate on any specific aspect of these analyses or their results?