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L26 Persistent and Long Memory Processes

Persistence

  • Persistence in time series: Tendency of past values to have a long-lasting influence on future values.
  • It's the degree of memory a TS has, i.e. how long shocks or disturbances to the system affect future observations.

If the influence of a shock (a spike in the stock price) has a long-lasting effect on the stock of the price in the future.

Characteristics

Characteristic
Long Term Impact Shock will have an influence that decays slowly over time
Autocorrelation decay Short-memory process (ARMA): ACF drops off rapidly. Vs here.
Long vs short memory Long-memory (persistent) process: like that modelled by ARFIMA → slow, hyperbolic decay in ACF.
VS
short-memory → Quickly approaches zero.
#### Examples
  • Financial markets: sharp rise → continue to be influenced by the rise
  • Environmental data: yesterday was rain \(\implies\) today would also be rain
  • Economics → GDP rise. Economic shocks have long-lasting effects

Importance

  • Forecasting: persistent series require ARFIMA (which account for long memory)
  • Risk Management: large fluctuations are likely to persist.

In Financial Markets

  • Stock Market returns
    • Sudden surge in price due to a positive earning report (information)
    • This effect would last for some time and remain elevated for a longer time.
  • Prolonged period of positive (or negative) return
  • This suggests momentum effect. Trends continue for some time.

  • Conversely, in non-persistent markets, price movements quickly reverse → mean reverting process

  • Volatility Clustering

    • during a financial crisis → market volatility suddenly increases
    • large price movements \(\implies\) more large movements in the future
  • Crucial for risk management
  • Periods of high risk (large price swings) are not isolated. They last.

  • This also has an impact on option pricing \(\implies\) Complexity in accurately pricing options.

  • Interest Rates

    • This exhibit persistence, in long-term yields
    • Effect of a policy by central bank on interest rates, will persist for a long time, influence borrowing costs, savings and decisions.
  • This is also critical for bond pricing, bonds are sensitive to changes in interest rates.
  • Long-term rates (10-year government of India bond) can complicate forecasting.

In Environmental Data

  • Temperature Persistence (Global Warming)

    • Higher-than-average temperatures in one year are followed by the same.
    • Affects ecosystems, weather patterns and human health.

  • Precipitation and drought persistence

    • below-average precipitation continues
    • dry years followed by more dry years

Anti-persistent Time Series

  • Anti-persistent or mean reverting TS
    • increase will be followed by a decrease and vice versa
  • Characterized by a negative autocorrelation structure.