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stats_model_jupyter

Time series are all around us, from stock prices and weather forecasts to economic trends and medical diagnoses. This course is designed to equip you to effectively model, interpret, and forecast time series.

In this course, you’ll learn time series analysis concepts, such as stochasticity, stationarity, and autocorrelation. You’ll analyze the time series by computing its various moments and by visualizing it using histogram and density plots. Next, you’ll decompose the time series into its trend, season, and cycle components. You’ll then learn about linear time series models, including autoregressive (AR) processes, moving average (MA) processes, ARMA, and ARIMA. You’ll fit these models on data and forecast the future and finish with evaluating the models using various goodness of fit criteria. 

By the end of this course, you’ll have a solid foundation in univariate time series analysis and the skills to explore, model, and forecast time series data using Python.

An Introduction to Time Series

**(True or False)** The autocorrelation function (ACF) and partial autocorrelation function (PACF) of a series will always tell us the order of the seasonal and non-seasonal parameters of a SARIMA model. 

(True or False) The autocorrelation function (ACF) and partial autocorrelation function (PACF) of a series will always tell us the order of the seasonal and non-seasonal parameters of a SARIMA model.

MLE is a technique to find the parameter values of a statistical model by minimizing the likelihood of observing the training data.

MLE is a technique to find the parameter values of a statistical model by maximizing the likelihood of observing the training data.

MLE is a technique to find the parameter values of a statistical model that uses random value selection (RVS) to find the values that maximize the likelihood of observing the training data.

MLE is a mathematical formula used to calculate the mean of the observed data.

What is maximum likelihood estimation (MLE)?

What is maximum likelihood estimation (MLE)?

Lower values of both AIC and BIC indicate a better-fitting model. 

Higher values of both AIC and BIC indicate a better-fitting model.

Lower values of both AIC and BIC indicate lower computational efficiency of a model. 

The AIC and the BIC are an average of the p-values of the model parameters. 

How would you interpret the values of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC)? 

How would you interpret the values of the Akaike information criterion (AIC) and the Bayesian information criterion (BIC)?

Randomly splitting the data undermines the assumption of stationarity in time series.

Randomly splitting the data disrupts the temporal order necessary for time series analysis.

Randomly splitting the data might introduce bias and skew the model's performance evaluation.

Randomly splitting the data might cause models to overfit to future observations.

Why is it *not* appropriate to randomly split the data into train, validation, and test sets for time series forecasting?

Why is it not appropriate to randomly split the data into train, validation, and test sets for time series forecasting?

We can use the data from January 2015 till December 2021 as the train set and the rest of the data as the test set.

We can stratify the data into four folds of the same length and train the model using standard cross-validation.

We can use the data from January 2015 till December 2015 as the test set and the rest of the data as the train set.

We can divide the data into multiple train-test folds, where each fold's test set contains consecutive months following the train set.

Suppose you’ve got a time series with monthly data from January 2015 to December 2022. How would you split it into train and test sets to train an ARIMA model?  

Suppose you’ve got a time series with monthly data from January 2015 to December 2022. How would you split it into train and test sets to train an ARIMA model?

All model parameters are statistically significant. 

The residuals of the model are normally distributed.

The residuals are independent, i.e., they are not autocorrelated. 

**(Select all that apply.)** Which assumption about our model can we test by analyzing its residuals?

(Select all that apply.) Which assumption about our model can we test by analyzing its residuals?

```Python
model = model.amplify([obs], refit = False)
```

```Python
model = model.append([obs], refit = False)
```

```Python
model = model.extend([obs], refit = False)
```

```Python
model = model.append([obs], refit = True)
```

**(Select all that apply.)** How would you update the data in an `ARIMAResults` object called `model` with the newest observation of the time series that it models called `obs`?

(Select all that apply.) How would you update the data in an <code>ARIMAResults</code> object called <code>model</code> with the newest observation of the time series that it models called <code>obs</code>?

It is always better, as its MSE is smaller than model 2's MSE.

It is always worse, as its MSE is smaller than model 2's MSE.

It is better than model 2 for a rolling one-step-ahead forecast, but it might not be so for other forecast horizons. 

To say which model is better for out-of-sample forecasting, we would need to know their AIC or BIC. 

Suppose you have trained two SARIMA models. Model 1 has an out-of-sample MSE of 3.1 on its rolling one-step-ahead forecast. Model 2 has an equivalent MSE of 3.4. Is model 1 better or worse than model 2 for out-of-sample prediction?

Suppose you have trained two SARIMA models. Model 1 has an out-of-sample MSE of 3.1 on its rolling one-step-ahead forecast. Model 2 has an equivalent MSE of 3.4. Is model 1 better or worse than model 2 for out-of-sample prediction?

Quiz yourself on choosing, fitting, and evaluating ARIMA models. 

Quiz

Quiz yourself on choosing, fitting, and evaluating ARIMA models.

Introduction to Time Series

The Basics of Time Series

Exploring Data

The Properties of Time Series

ARIMA Models

On Prediction

Choosing, Fitting, and Evaluating Models

Conclusion

Appendix

What have you learned?

Quiz