In summer 2019, high water levels wreaked havoc on the communities bordering the Great Lakes leading to widespread damage in coastal cities, eroding shorelines and beaches. In May'2019, Lake Erie hit its highest average monthly water level since 1918. Cleveland, Ohio on Lake Erie’s shore saw more rainy days than any year since 1953.

In this study, we will use Mean Water Level data for Lake Erie, Precipitation data for Erie basin (land+lake) and Mean Air Temperature data over Lake Erie to understand trends and forecast how water levels will vary into the future. We will explore various Univariate and Multivariate Time Series modeling techniques such as:

  • Exponential Smoothing Models
  • ARIMA (Autoregressive Integrated Moving Average) Models
  • SARIMA (Seasonal Autoregressive Integrated Moving Average) Models
  • VARMA (Vector Autoregressive Moving Average) Models

Part-1 Exponential Smoothing Models
In this notebook, we will:

  • Read Lake Erie water level data
  • Perform datatime operations to index it as a time series
  • Explore the data
  • Decompose data to separate the trend and seasonality components
  • Built and fit different Exponential Smoothing models on the data
    • Simple Exponential Smoothing
    • Double Exponential Smoothing
    • Triple Exponential Smoothing
  • Perform prediction on test data and evaluated model performance
    • Split the data
    • Fit models
    • Generate predictions
    • Evaluate model performance

Part-2 ARIMA Models
In this notebook, we will:

  • Read Lake Erie water level data and index it as a time series
  • Discuss Stationarity of data
  • Difference the data to make it stationary
  • Use the ACF and PACF plots to decide AR term(s) and MA term(s) for ARIMA model
  • Identify optimal ARIMA order using grid search.
  • Split the data
  • Built and fit optimal ARIMA model
    • Obtain Predictions
  • Evaluate Model performance
    • Plot predictions and calculate loss
  • Forecast for 100 months into the future

Part-3 Seasonal ARIMA Models
In this notebook, we will:

  • Read Lake Erie water level data and index it as a time series
  • Discuss Stationarity of data
  • Difference the data to make it stationary
    • Seasonal first order differencing
    • Seasonal and Non-seasonal first order differencing
  • Use the ACF and PACF plots to decide AR term(s) and MA term(s) for SARIMA model
  • Identify optimal SARIMA (p,d,q) x (P,D,Q) order using grid search
  • Split the data
  • Built and fit optimal SARIMA model
    • Obtain Predictions
  • Evaluate Model performance
    • Plot predictions and calculate loss
  • Forecast for 100 months into the future

Part-4 VARMA Models
In this notebook, we will:

  • Read Water level, Precipitation and Air Temperature data for Lake Erie and index it as a time series
  • Discuss Stationarity of data
  • Difference the data to make it stationary
  • Identify optimal VARMA(p,q) order using grid search
  • Split the data
  • Built and fit optimal VARMA model
    • Obtain Predictions
  • Evaluate Model performance
    • Plot predictions and calculate loss
Language: Python