Time Series Analysis: Stationarity and Forecasting

Module: Machine Learning | Difficulty: Advanced

Stationarity

AR(p) Model

MA(q) Model

ADF Test

: (unit root, non-stationary)

Spectral Density

import numpy as np
from statsmodels.tsa.arima.model import ARIMA

class ARIMAForecast:
    def __init__(self, order=(1,1,1)):
        self.order = order; self.model = None
    def fit(self, y):
        self.model = ARIMA(y, order=self.order).fit()
    def forecast(self, steps=10):
        return self.model.forecast(steps=steps)
    def aic(self):
        return self.model.aic

| Method | Stationarity | Nonlinear | Long-term | |--------|-------------|-----------|-----------| | ARIMA | Required | No | Poor | | Prophet | Optional | Limited | Good | | LSTM | Optional | Yes | Good | | Transformer | Optional | Yes | Excellent |

Research Insight: Transformer-based forecasting (Informer, Autoformer) outperform traditional methods on long sequences because attention captures long-range dependencies. However, they require large datasets and can overfit on short series.