I've read articles, journals and books regarding long memory property of a time series data. And most of it found that, it is common in financial and economic perspective. I know , for example, in exchange rates, if the autocorrelation function of the series decays slowly to zero then it might have long memory property. But my question is why? What is in financial and economic data that it mostly exhibit long memory property? Anyone has an idea?
Finance and economics are ruling our subconscious mind today. It is this quality of the financial and economic data along with human hoarding causing insecurity that our neurons are exhibiting long memory property regarding such data.
Jane,
it's worth mentioning that the so called "long memory" as a scientific term can be actually viewed rather as a metaphor.
For more about the history of the concept see the link below.
Best regards
http://www.long-memory.com/
I am not sure whether I understand the question. Long memory is a statistical properly that might be present in time-series data. If you google something like "long memory time series", you might find mostly economics and finance papers. However, this reflects first of all the fact that finance and economics is maybe being researched more than other fields. For example, Hurst exponent is named after Harold Edwin Hurst who documented long memory in hydrology.
Long memory was coined early in the study of time series data soon after Student discovered the t distribution with a constant range measure sigma/Sqrt(n) or the stationary standard deviation. As Constant standard deviation in the errors is hardly ever observed because of auto correlations,
In Financial data we typically also understand the long range dependence as the slowness of markets to digest information introduced to efficient markets in the noise around prices.
mandelbrot observed and denoted the Noah effect and the long tails including the Hurst effect in statistical properties of various econometric data
Following typical features are refered in the included text for time series data
1. Spurious trends, cycles and self similarities(autocorrelations)
2 Slow hyperbolic decay(also auto correlations)
Hurst defined long range dependence earliest in hydrology where he uses the R/S statistic as the standardised capacity of a reservoir
Specific to Economics and Finance, the Financial market model is well explained in the following reference Ding, Engel and Granger (1993)
As the literature in the paper explains, there are substantial autocorrelations in returns against the Efficient Markets seemingly but in line with the fair game theory, As Mandelbrot observed fairly early on, these returns are themselves seemingly not serially correlated but the |r| or the absolute value of these returns is substantially correlated. This also explains the mean reversion property of returns yet they are not iid and hence the long memory property linked to the material improvement in financial modeling by the recognition of heteroskedasticity.
iid= identically and independently distributed
Jane:
In finance, long memory property of time series is often related to the increased share of equities by institutional investors (e.g. because they distribute their trades over time to lower their price impact... inducing an increase in stock return autocorrelation)
More details can be found here:
https://www.researchgate.net/publication/227653983_The_impact_of_institutional_investors_on_risk_and_stock_return_autocorrelation_in_the_context_of_the_polish_pension_reform
Best regards
Article The impact of institutional investors on risk and stock retu...
To put it very simply, Financial and Economic data exhibit long memory because fundamentally their future values depend to a significant extent on their past values. For example: In Stock markets, further investments are often made on the basis of technical analysis of past prices and volume information. We buy undervalued stocks and sell overvalued ones. So, present stock prices will show long memory or dependence on past. In Economic data, GDP growth rate and inflation rate are directly dependent on past value. Higher the base, lower is rate of change (base effect). Also, certain economic phenomenon's effect materialises only after certain lag example effect of rate cut by central banks or investment announcements.
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