Time series analysis

Time Series Analysis is a statistical method used to analyze data points collected over a period of time. The data points are typically recorded at consistent intervals (e.g., daily stock prices, hourly temperature readings, monthly sales figures). The goal is to understand the underlying patterns, trends, and components within the data and often to make forecasts about future values.

Time Series Analysis helps identify and quantify various characteristics within sequential data, such as:

• **Trends:** Long-term upward or downward movements.
• **Seasonality:** Regular patterns that repeat over fixed periods (e.g., daily, weekly, monthly, yearly).
• **Cycles:** Longer-term fluctuations not tied to a specific fixed period.
• **Irregular/Random Variations:** Unpredictable movements.
• **Autocorrelation:** The relationship between a data point and previous data points.

By understanding these components, analysts can interpret past behavior and predict future values.

Performing time series analysis typically involves several steps:

1. **Data Collection & Cleaning:** Gathering the sequential data and handling missing values or errors.
2. **Visualization:** Plotting the data over time to visually identify patterns, trends, and seasonality.
3. **Decomposition:** Separating the time series into its core components (trend, seasonality, residual/irregular).
4. **Model Selection:** Choosing an appropriate statistical or machine learning model (e.g., ARIMA, Exponential Smoothing, Prophet, time series regression, deep learning models).
5. **Model Fitting & Evaluation:** Training the model on historical data and assessing its performance using metrics like Mean Squared Error (MSE) or Root Mean Squared Error (RMSE).
6. **Forecasting:** Using the fitted model to predict future values.

A typical time series is often considered a combination of several components:

• **Trend:** The overall long-term direction of the data (upward, downward, or horizontal).
• **Seasonality:** Patterns that repeat regularly within a fixed period (e.g., retail sales peaking during holidays).
• **Cyclical Component:** Long-term fluctuations that are not seasonal and may be due to economic cycles (e.g., recessions). Their duration is typically longer than a year and not of fixed length.
• **Irregular (or Random) Component:** Unpredictable variations in the data that cannot be explained by trend, seasonality, or cycles.

These components can be combined additively or multiplicatively depending on the nature of the data.

Time series analysis is widely used across many fields, including:

• **Finance:** Stock price forecasting, economic indicator analysis (GDP, inflation), risk management.
• **Business:** Sales forecasting, inventory management, demand planning, resource allocation.
• **Economics:** Predicting economic growth, unemployment rates, market trends.
• **Meteorology:** Weather forecasting, climate change analysis.
• **Science & Engineering:** Signal processing, environmental monitoring, sensor data analysis.
• **Healthcare:** Disease outbreak prediction, patient monitoring.

It's essential whenever understanding historical patterns over time is needed to inform future decisions.

Stationarity is a key concept. A stationary time series is one whose statistical properties (like mean, variance, and autocorrelation) remain constant over time, regardless of the period being examined.

Many time series models (like ARIMA) assume stationarity. Non-stationary data often needs to be transformed (e.g., differencing to remove a trend) to become stationary before these models can be applied effectively. Stationarity simplifies modeling because the process generating the data is assumed to be consistent over time.