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Peter Westfall is a professor at Texas Tech University. He specializes in using statistics in investing, technical analysis, and trading.
What Is Heteroskedasticity?
In statistics, heteroskedastiđô thị (or heteroscedasticity) happens when thestandard deviations of a predicted variable, monitored over different values of an independent variable or as related khổng lồ prior time periods, are non-constant. With heteroskedasticity, the tell-tale sign upon visual inspection of the residual errors is that they will tover khổng lồ fan out over time, as depicted in the image below.
Heteroskedastithành phố often arises in two forms: conditional và unconditional. Conditional heteroskedasticity identifies nonconstant volatility related lớn prior period"s (e.g., daily) volatility. Unconditional heteroskedastiđô thị refers to general structural changes in volatility that are not related to prior period volatility. Unconditional heteroskedastithành phố is used when future periods of high and low volatility can be identified.
In statistics, heteroskedastithành phố (or heteroscedasticity) happens when the standard errors of a variable, monitored over a specific amount of time, are non-constant.With heteroskedasticity, the tell-tale sign upon visual inspection of the residual errors is that they will tkết thúc lớn tín đồ out over time, as depicted in the image above.
While heteroskedasticity does not cause bias in the coefficient estimates, it does make them less precise; lower precision increases the likelihood that the coefficient estimates are further from the correct population value.
The Basics of Heteroskedasticity
In finance, conditional heteroskedasticity is often seen in the prices of stocks & bonds. The màn chơi of volatility of these equities cannot be predicted over any period. Unconditional heteroskedastiđô thị can be used when discussing variables that have identifiable seasonal variability, such as electriđô thị usage.
As it relates lớn statistics, heteroskedasticity (also spelled heteroscedasticity) refers to lớn the error variance, or dependence of scattering, within a minimum of one independent variable within a particular sample. These variations can be used lớn calculate the margin of error between data sets, such as expected results and actual results, as it provides a measure of the deviation of data points from the mean value.
For a datamix to be considered relevant, the majority of the data points must be within a particular number of standard deviations from the mean as described by Chebyshev’s theorem, also known as Chebyshev’s ineunique. This provides guidelines regarding the probability of a random variable differing from the mean.
Based on the number of standard deviations specified, a random variable has a particular probability of existing within those points. For example, it may be required that a range of two standard deviations contain at least 75% of the data points to lớn be considered valid. A comtháng cause of variances outside the minimum requirement is often attributed khổng lồ issues of data unique.
The opposite of heteroskedastic ishomoskedastic. Homoskedasticity refers khổng lồ a condition in which the variance of the residual term is constant or nearly so. Homoskedastiđô thị is one assumption of linear regression modeling. It is needed lớn ensure that the estimates are accurate, that the prediction limits for the dependent variable are valid, & that confidence intervals và p-values for the parameters are valid.
The Types Heteroskedastiđô thị
Unconditional heteroskedastiđô thị is predictable and can relate khổng lồ variables that are cyclical by nature. This can include higher retail sales reported during the traditional holiday shopping period or the increase in air conditioner repair calls during warmer months.
Changes within the variance can be tied directly lớn the occurrence of particular events or predictive sầu markers if the shifts are not traditionally seasonal. This can be related to lớn an increase in điện thoại thông minh sales with the release of a new Model as the activity is cyclical based on the sự kiện but not necessarily determined by the season.
Heteroskedastithành phố can also relate lớn cases where the data approach a boundary—where the variance must necessarily be smaller because of the boundary"s restricting the range of the data.
Conditional heteroskedastiđô thị is not predictable by nature. There is no telltale sign that leads analysts to lớn believe sầu data will become more or less scattered at any point in time. Often, financial products are considered subject to lớn conditional heteroskedastithành phố as not all changes can be attributed to lớn specific events or seasonal changes.
A comtháng application of conditional heteroskedastiđô thị is to lớn stochồng markets, where the volatility today is strongly related lớn volatility yesterday. This Mã Sản Phẩm explains periods of persistent high volatility & low volatility.
Heteroskedastiđô thị và Financial Modeling
Heteroskedasticity is an important concept in regression modeling, và in the investment world, regression models are used khổng lồ explain the performance of securities và investment portfolgame ios. The most well-known of these is theCapital Asphối Pricing Model (CAPM), which explains the performance of a stoông chồng in terms of its volatility relative sầu to the market as a whole. Extensions of this model have added other predictor variables such as kích thước, momentum, chất lượng, & style (value versus growth).
These predictor variables have been added because they explain or trương mục for variance in the dependent variable. Portfolio performance is explained by CAPM. For example, developers of the CAPM model were aware that their model failed to explain an interesting anomaly: high-quality stocks, which were less volatile than low-unique stocks, tended to lớn persize better than the CAPM model predicted. CAPM says that higher-risk stocks should outpersize lower-risk stocks.
In other words, high-volatility stocks should beat lower-volatility stocks. But high-chất lượng stocks, which are less volatile, tended to perform better than predicted by CAPM.
Later, other researchers extended the CAPM Model (which had already been extended lớn include other predictor variables such as kích thước, style, & momentum) lớn include chất lượng as an additional predictor variable, also known as a "factor." With this factor now included in the Model, the performance anomaly of low volatility stocks was accounted for. These models, known asmulti-factor models, size the basis offactor investing& smart beta.