Time Series Analysis

What?

Time series analysis is a crucial tool in financial markets used to study and forecast the behaviour of various financial variables like stock prices, interest rates and exchange rates.

A time series refers to a collection of data points recorded at different time intervals for a particular variable. Examples include a company’s quarterly sales, daily stock returns, or monthly currency exchange rates. What sets time series data apart is that each observation is tied to a specific point in time, maintaining a chronological order.

Characteristics

Time series data often shows specific patterns that are important to recognise for accurate analysis and forecasting:

  1. Trends: These are long-term movements in the data, showing a consistent rise or fall over time.
  2. Seasonality: Time series may follow recurring patterns at fixed intervals, such as daily, weekly, or yearly, due to seasonal effects.
  3. Volatility: Some time series fluctuate significantly and unpredictably, with sharp changes in values over short periods.
  4. Non-linearity: The relationship between time and the variable may not follow a straight line, making it challenging to capture with simple linear models.

https://youtu.be/GE3JOFwTWVM?si=ejA-RpfaKJ4nvE6s

Stationarity

Types of Stationarity

Stationarity in time series comes in different forms, depending on which aspects of the data remain stable over time:

  1. Strict Stationarity: This is the most rigid form. It means the entire distribution of the data, including the mean, variance, and even higher moments like skewness, stays exactly the same no matter when you observe it. In practice, it's extremely rare to find real-world data that meets this condition.
  2. First-Order Stationarity: Here, only the average value (the mean) of the series remains fixed over time. Other properties, like variance or how spread out the values are, can still shift.
  3. Second-Order (Weak) Stationarity: This is the most commonly used type. It assumes that the mean and variance stay the same throughout, and the relationship between data points (captured by autocovariance) depends only on how far apart they are in time, not when they occur.

Why Stationarity Matters?

When working with time series data, one of the most important things to check is whether the data is stationary. If the data is non-stationary, it can throw off the results leading to unreliable predictions.

https://youtu.be/oY-j2Wof51c?si=WZJQ4I7wLxA-WFsd