You've plotted the drama, spotted the trends, and smoothed the chaos. Now for the truly depressing part: attempting to predict the future. Time series analysis isn't just about understanding the past; it's about using that past to forecast what comes next. Will your relationship happiness continue its downward spiral? Will your screen time finally consume your soul? Basic forecasting tries to answer these questions using simple models.
One of the most basic forecasting methods is the Naive Forecast. It assumes the next value will simply be the same as the last observed value. Utterly simplistic, often wrong, but a starting point. A slightly more sophisticated approach might involve extending the observed trend. However, as anyone who has lived through unpredictable systems (like the internet or human emotions) knows, the future rarely cooperates with simple predictions.
Algorithms constantly forecast your behavior to serve you the next piece of content, the next targeted ad, the next notification. They use far more complex models than we'll cover here, but the principle is the same: predict what you'll do next based on what you've done before. Understanding basic forecasting shows you how these predictions are made, and why, despite their sophistication, they can never truly capture the glorious, messy unpredictability of genuine human (or systemic) chaos.
Let's see a simple forecast applied to our happiness data. Observe the dashed line extending into the future – a prediction based on the past, likely doomed to be inaccurate.
The Naive Forecast for the next time period ($t+1$) is simply the value observed in the current time period ($t$).
$\hat{y}_{t+1} = y_t$
Where $\hat{y}_{t+1}$ is the forecast for time $t+1$, and $y_t$ is the actual value at time $t$.
Using our example data $Y = \{8, 7, 6, 7, 5, 4, 6, 5, 4, 3\}$, the last observed value is $y_{10} = 3$.
A Naive Forecast for week 11 would be $\hat{y}_{11} = y_{10} = 3$.
This method assumes no change from the last observation. It's a baseline to compare more complex forecasts against.
A slightly more complex approach is to extend a previously identified trend. If we fit a linear trend to the data (as conceptually shown in Module 2), we can use the equation of that line to predict future values.
Using a simple linear trend model: $\hat{y}_{t+k} = a + b(t+k)$
Where $a$ and $b$ are the intercept and slope of the trend line, $t$ is the last observed time point, and $k$ is the number of periods into the future you are forecasting.
Our visualization shows a simple extrapolation from the last data point, following the direction towards the last point from the one before it. This is a very basic form of trend extension.
Basic forecasting methods like these often fail because real-world time series are influenced by many factors beyond simple past values or trends. They don't account for:
While algorithms use more advanced techniques (like ARIMA, Prophet, or machine learning models), they are still making educated guesses based on past data. The future, especially in chaotic systems, remains inherently uncertain. Your predicted misery might arrive, but perhaps not exactly when or how the algorithms (or this lesson) suggest.