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struct.txt
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struct.txt
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Task List:
A. Pre-processing data:
- [X] Convert column types
- [X] Reindex dataframe starting at 0 for 1958-01-01 and adding 1 for every month
- [X] Split the data into training and test datasets using 80:20 split
- [X] Drop data points recorded as -99.99
[X] Completed
B. Detrending:
- [X] Fitting the training data to a simple linear model F = alpha_0 + alpha_1*t to estimate the long-term trend F
- [X] Estimate values for alpha_0 and alpha_1 using scikit-learn LinearRegression()
- [X] Plot the residual errors R = C - F
- [X] Calculate the RMSE and MAPE with respect to the test set for the model
- [X] Fitting a quadratic model to the data F = beta_0 + beta_1*t + beta_2*t**2 to estimate the long-term trend F
- [X] Estimate values for beta_0, beta_1, and beta_2
- [X] Plot the residual errors R = C - F
- [X] Calculate the RMSE and MAPE with respect to the test set for the model
- [X] Fitting a cubic model to the training data F = gamma_0 + gamma_1*t + gamma_2*t**2 + gamma_3*t**3
- [X] Estimate values for gamma_0, gamma_1, gamma_2, and gamma_3
- [X] Plot the residual errors R = C - F
- [X] Calculate the RMSE and MAPE with respect to the test set for the model
- [?] Model Selection
- [?] Plot the residual errors side by side for each of the three models
- [X] Compare the RSME and MAPE for the three models
- [X] Select the best models based on the two conditions above
[X] Completed
C. Unseasoning:
- [X] Remove the deterministic trend F from the time series
- [X] Group by month
- [X] Calculate the average signal for each month
- [X] Plot the periodic signal Pi against time
[X] Completed
D. Aggregate Model with Trend and Seasonality:
- [ ] Create the final function for CO2 concentration: C = F + P
- [ ] Make the prediction using C and plot it on top of the actual data, indicating the split between the training and testing data
- [ ] Calculate the final RMSE and MAPE with respect to the test set
- [ ] Plot the Aggregate model side by side with the one without the periodic signal
- [ ] Calculate the ratio of the range of the values of F to the amplitude of P for each month
- [ ] Calculate the ratio of the range of the values of P to the range of the residuals
[ ] Completed
E. Autocovariance Function:
- [ ] Create a new dataframe that has removed trend and seasonality
- [ ] Compute PACF and ACF before models
- [ ] Fit a MA(1) model to the data
- [ ] Obtain the model parameters using statsmodels.tsa.arima.model.ARIMA
- [ ] Plot PACF and ACF side by side to the before model
- [ ] Evaluate the fitted models using AIC and BIC
- [ ] Conduct residual analysis to check for any remaining patterns in the residuals
- [ ] Fit an AR(1) model to the data
- [ ] Obtain the model parameters using statsmodels.tsa.arima.model.ARIMA
- [ ] Plot PACF and ACF side by side to the before model
- [ ] Evaluate the fitted models using AIC and BIC
- [ ] Conduct residual analysis to check for any remaining patterns in the residuals
[ ] Completed