A Complete Guide to Time Series Models.

1. Understanding Time Series Data

What is Time Series?

Time series is a sequence of data points ordered in time or a set of observations taken at specified times, usually at equal intervals. The data can be univariate, that is a single variable over time or multivariate where multiple variables are observed over time. Examples of these are stock prices, temperature measurements etc.
Times series models on the other hand are models that are used to analyze and forecast the future.

Components of Time Series Data

1.Trend: This is the movement of data to relatively higher or lower values over a long period of time. It can be upward (uptrend), downward (downtrend), or flat (stationary trend).
2.Seasonality: Here the data shows repeating patterns at fixed intervals, such as daily, weekly, or yearly.
3.Noise: The data is erratic in nature and shows random fluctuations that cannot be attributed to the trend or seasonality. It represents the irregular, unpredictable components of the data.
4.Cyclic: This is the repeating up and down movement within the data with no predictable pattern.

2. Types of Time Series Models

• Descriptive Analysis: aims to identify patterns in time series data like trends, seasonal variation and cycles.
• Time Series Forecasting: involves predicting future data based on historical trends. Various models, such as ARIMA and Exponential Smoothing, are used for this purpose.
• Explanative Analysis: explores cause-and-effect relationships in time series data. Granger Causality and Vector Autoregression (VAR) are common techniques.
• Classification: Identifies and assigns categories to the data.
• Curve fitting: Plots the data along a curve to study the relationships of variables within the data
• Segmentation: Splits the data into segments to reveal the underlying properties of the source information

3. Preprocessing Time Series Data

Data Collection and Cleaning: Collect and clean your time series data. This may involve dealing with missing values, outliers, and data format issues.
Handling Missing Data: Various techniques can be employed to fill in missing values such as median for numerical values and mode for categorical data types.
Resampling and Aggregating: Adjust the time intervals of your data, especially when dealing with irregularly spaced time series. Common methods include resampling and aggregation.

4. Exploratory Data Analysis (EDA)

In this step one create time plots to visualize the data, including the trend and seasonality. Decomposition is then done where the time series is deconstructed into its trend, seasonality, or residual components. There are two main types of decomposition: decomposition based on rates of change and decomposition based on predictability. Lastly check if the time series is stationary, meaning the mean and variance remain constant over time. Non-stationary data may require differencing. Stationarity can be checked in two ways;

1. The Dickey-Fuller Test is a statistical test that is used to check for null hypothesis which shows if the time series is non-stationary.
2. Rolling statistics by plotting the moving average or moving variance to see if it varies with time.

5. Time Series Modeling Techniques

Moving Averages
Moving average model is a common approach for modeling univariate time series. It smooths out the noise in the data by stating that the next observation is the mean of all observations. This helps identify trends and seasonality.

Exponential Smoothing
Exponential smoothing assigns exponentially decreasing weights to past observations, giving more importance to recent data points.

ARIMA (AutoRegressive Integrated Moving Average)
ARIMA combines autoregressive (AR) and moving average (MA) components, with differencing to make the time series stationary. AR is denoted by p, when p = 0 there is no correlation in the series and when p = 1 then the auto-correlation is up to one lag.
MA on the other hand is denoted by q. When q =1 it means there is an error term.
Integration in the model is denoted by d. When d = 0 the series is stationary and non-stationary when d = 1.

Seasonal ARIMA (SARIMA)
This modeling technique extends ARIMA to handle seasonal components in the data by adding a linear combination of seasonal past values and /or forecast errors.

6. Model Evaluation and Deployment.

The models chosen need to have their performance evaluated. This is done by splitting the data into training and testing sets. Forecast accuracy is evaluated using metrics like Mean Absolute Error (MAE), Mean Squared Error (MSE), and Root Mean Squared Error (RMSE). Finally to ensure your model generalizes well we perform time series cross-validation.
Once the models have been evaluated, choose the most appropriate model and fine-tune parameters. Avoid overfitting (overly complex models) and underfitting (overly simplistic models) by selecting the right complexity. Detect and deal with outliers in your data, which can distort your models.
Once a model is trained and evaluated, deploy it for making real-time predictions or automated forecasts.

Tools; Python and R are popular programming languages for time series analysis. Various libraries are available, such as Pandas, Statsmodels, Prophet, forecast, and fable.