### Introduction

Imagine you have collected data points like temperatures measured every hour for a week or stock prices recorded every day for 6 months. Time series is when you organize this data based on time. Each data point is associated with time. So, time series is just a fancy term for data organized in order of time. In other words, a time series is a sequence of observations or measurements collected and recorded at successive, evenly-spaced intervals over a defined period. It can also be defined as data points associated with a timestamp, representing when the observation was made.

In contrast to time series data, other types of data don't have this sequential structure, such as cross-sectional or panel data. Here, each observation represents a different individual, entity, or location. Though it captures over a period of time, it's not strictly ordered by time. For instance, if you survey people from different cities about their favourite food, each person's response constitutes a single observation, and there's no inherent time order to these observations.

Let's get back to the time series.

Studying how things change over time by analyzing data collected and recorded in a systematic way is called time series analysis. It involves examining the data's patterns, trends, and behaviours to uncover insights, make predictions, or understand the underlying processes driving the observed changes over time.

For instance, you might have a list of numbers representing your monthly sales figures. First, you might look for trends, like whether the numbers generally go up, down, or stay the same over time.

You could also check for seasonal patterns, like if certain numbers tend to rise or fall at certain times of the year, such as holiday shopping spikes. Then, you might want to predict what will happen in the future based on what's happened in the past. This could involve using mathematical models or algorithms to forecast future values, which can be super helpful for planning and decision-making.

Finally, time series analysis can help you spot any unusual events or outliers in the data. These could be sudden spikes or drops that don't fit the usual pattern, which might signal something interesting or important.

Time series analysis typically involves data visualization, trend estimation, forecasting, and anomaly detection. It finds applications across various fields, including economics, finance, weather forecasting, engineering, and healthcare. Governments and policymakers use time series analysis to analyze economic indicators, monitor population trends, and evaluate the effectiveness of policies or interventions.

### Analyzing Time Series Data

Analyzing time series data involves several steps and techniques to uncover patterns, trends, and relationships within the data. The following are steps to analyze the time series:

1. Data Exploration and Visualization
Begin by collecting and recording your time series data to understand its structure, variables, and missing values. Visualize the data using line charts, histograms, and box plots to identify patterns, trends, and anomalies.
2. Descriptive Statistics
Next, do some math to describe your data. Calculate descriptive statistics like the average, median, standard deviation, and percentiles. Relate today's data with yesterday's or last week's to gain insights into the degree of similarity, variability, and distribution of the data.
3. Trend Analysis:
Here, we identify the long-term changes in data. This can involve fitting trend lines or curves to the data using techniques such as linear regression, polynomial regression, or exponential smoothing.
4. Seasonal Decomposition:
Sometimes, your data might change depending on the time of year, like more ice cream sales in summer. Separate your data into parts: the overall trend, the repeating seasonal patterns, and any leftover surprises. We can analyze the seasonal patterns using methods like seasonal decomposition of time series (STL) or seasonal-trend decomposition using LOESS (STL).
5. Spectral Analysis:
Decompose the time series into its frequency components using techniques like Fourier analysis or wavelet transforms to identify periodic patterns, cyclical behaviours, or dominant frequencies within the data.
6. Forecasting:
This process involves predicting what will happen in the future based on what's happened in the past. Various forecasting methods include statistical models like ARIMA (Autoregressive Integrated Moving Average), exponential smoothing, and machine learning algorithms such as neural networks and random forests. The accuracy of the forecast can also be calculated using metrics like mean absolute error (MAE), mean squared error (MSE), or root mean squared error (RMSE).
7. Anomaly Detection:
Anomaly detection looks for anything strange or unexpected in your data, like outliers or unusual patterns. This can involve statistical methods, such as Z-score analysis or time series decomposition, as well as machine learning approaches like isolation forests or autoencoder-based methods. You can further investigate the causes of anomalies and determine whether their presence is due to errors in the data or reflects genuine anomalies.
8. Granger Causality Analysis:
It is a statistical test that provides casual relationships between variables in time series data. It helps to determine if one time series can predict another based on past values.

Let us take two time series: X and Y.

When we say, "X Granger causes Y," it means that X's past values can better predict Y's current values than just using Y's past values.
For example, we're looking at sales data (Y) and marketing expenditure (X). If we find that past marketing expenditure helps predict future sales better than just looking at past sales data alone, we might say that marketing spending "Granger causes" sales.

In simpler terms, Granger causality analysis helps us figure out if one thing happening in the past can tell us something useful about what will happen in the future with another thing.
9. Model Evaluation and Validation:
This is the process of validating the performance of your time series. Did your predictions match what actually happened? Validations can be done using techniques like cross-validation or train-test splits. The accuracy, precision, recall, and other relevant metrics can be calculated to determine the effectiveness of the models. This helps you know if you're on the right track or need to adjust your methods. Based on the feedback, iterations and refinements of the model can be done.
10. Interpretation and Communication:
Finally, explain what you found to others in a way they can understand. Visualize your results using clear and intuitive charts, graphs, or dashboards to facilitate understanding and decision-making.

### Conclusion

Following these steps can reveal valuable insights hidden within your time series data. Understanding its patterns, trends, and relationships empowers you to make informed decisions and take strategic actions.

In the next part, we'll explore different types of time series data with modelling techniques for time series analysis.