Notes on time series analysis

A mindmap of time series analysis

mindmap
  root((Time Series Analysis))
    Databases
        TimeScaleDB
        InfluxDB
    Python tools
        Altair
        Pandas
        DuckDB
        Polars
        Scipy
        Gekko
        Matplotlib
    Core concepts
        Trend
        Cycle
        Variation
        Statistical movements
        Stationary and non-stationary
        Seasonality
        Auto-Correlation
    Forcasting
        Auto Regressive Integrated Moving Average - ARIMA
        Exponential smoothing

    

Core concepts explained visually

Time series

Observed values of the same variable collected at regular time intervals.

In the below example, revenue is the variable observed with a monthly time intervals given a year.

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 13000
    line [5000, 6200, 7900, 8800, 10300, 11500, 12200, 11600, 10800, 10300, 9000, 8200]

Time series analysis

The method of analyzing a timestamped dataset to observe/forecast/predict past and future values for the observed variable. Hence this analysis can be used as a decision support system.

Trend

Positive secular trend

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue (positive secular trend)"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 13000
    line [5000, 5200, 6100, 5900, 6800, 7500, 8200, 7900, 8600, 8400, 9100, 9500]

Negative secular trend

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue (negative secular trend)"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 20000
    line [14000, 13600, 13900, 13200, 13500, 12800, 13100, 12500, 12700, 12100, 11800, 11500]

Seasonality

Time series data can change depending on the seasons/seasonal pattern.

Seasonal positive secular trend

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue (seasonal postive secular trend)"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 20000
    line [14000, 13600, 14800, 14200, 15100, 15600, 15300, 14900, 15800, 15400, 15900, 16200]

Seasonal negative secular trend

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue (seasonal negative secular trend)"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 20000
   line [14000, 13200, 13900, 12800, 13500, 14100, 12600, 13200, 13800, 12400, 12900, 13300]

Cyclic

---
config:
    xyChart:
        width: 700
        height: 350
    themeVariables:
        xyChart:
            titleColor: "#ff0000"
---
xychart-beta
    title "Sales revenue (Cyclic trend)"
    x-axis [jan, feb, mar, apr, may, jun, jul, aug, sep, oct, nov, dec]
    y-axis "Revenue (in $)" 4000 --> 20000
    line [10000, 10800, 11900, 13200, 14300, 15100, 15500, 15400, 14800, 13900, 12800, 11700]

Resources

Here are some of the resources which helped me learn the basic concepts of time series analysis with no specific order.

Introduction to time series analysis

Lecture on time series analysis

Patterns and trends in time series plots

When I learn an interesting aspect of time series analysis, I will update this post. For now, time series analysis was fun learning. I have barely scratched the surface here.

More fun to be had!