ARMA: Auto Regressive Moving Average

ARMA(1,1) time series model

X_t = 0.5 X_t-1 + Z_t + 0.7 Z_t-1

• AR order: p = 1
• MA order: q=1
• Stationarity: |0.5|<1
• Invertibility: |0.7|<1

Assuming Z_t is white noise, the model is stationary and invertible.

ARMA Limitations

Anomaly Detection

Autoencoder for Anamoly Detection

Latent Space: Encoder f, Decoder g

Isolation Forest Algorithm

Gaussian Mixture Model

LSTM Long Short Term Memory

ARIMA

Auto Regressive - eg: sales depend on past sales

Integrated - Removing long term/ seasonal changes

MA - Fixing unexpected errors

X_t : current value of series

ϕ_i : AR coefficients

p : order of AR process

ε_t : white noise (random error)

Backward Pass in RNN

GRU / LSTM

RAE, RCNN and RvNN

Autocorrelation

• sequential data : text and language, audio
• analysis methods :
  • decomposition
  • correlation analysis
  • smoothing
  • forecasting
• window function
• STFT - short time fourier transform
• types of window
  • adjacent
  • overlapped
• hop size (25%)
• co-integration
• auto-covariance and auto-correlation