Statistics Glossary
`
`http://www.stats.gla.ac.uk/steps/glossary/index.html
`
`Main Contents
`
`Alphabetical index of all entries
`
`Basic Definitions
`Presenting Data
`Sampling
`Probability
`Random Variables &
`Probability Distributions
`Confidence Intervals
`
`Hypothesis Testing
`Paired Data, Correlation &
`Regression
`Design of Experiments & ANOVA
`Categorical Data
`Nonparametric Methods
`Time Series Data
`
`STEPS Glossary Web version revised and updated Sep 97 by Stuart G. Young.
`Download the free STEPS software from the STEPS Web site
`
`
`PAGE 1 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`http://www.stats.gla.ac.uk/steps/glossary/index.html
`
`Main Contents
`
`Alphabetical index of all entries
`
`Basic Definitions
`Presenting Data
`Sampling
`Probability
`Random Variables &
`Probability Distributions
`Confidence Intervals
`
`Hypothesis Testing
`Paired Data, Correlation &
`Regression
`Design of Experiments & ANOVA
`Categorical Data
`Nonparametric Methods
`Time Series Data
`
`STEPS Glossary Web version revised and updated Sep 97 by Stuart G. Young.
`Download the free STEPS software from the STEPS Web site
`
`
`PAGE 1 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`Statistics Glossary - time series data
`
`http://www.stats.gla.ac.uk/steps/glossary/time_series.html
`
`Time series data
`
`Time Series
`Trend Component
`Cyclical Component
`Seasonal Component
`Irregular Component
`Smoothing
`
`Exponential Smoothing
`Moving Average Smoothing
`Running Medians Smoothing
`Differencing
`Autocorrelation
`Extrapolation
`
`Main Contents page | Index of all entries
`
`Time Series
`
`A time series is a sequence of observations which are ordered in time (or space). If
`observations are made on some phenomenon throughout time, it is most sensible to
`display the data in the order in which they arose, particularly since successive
`observations will probably be dependent. Time series are best displayed in a scatter
`plot. The series value X is plotted on the vertical axis and time t on the horizontal axis.
`Time is called the independent variable (in this case however, something over which
`you have little control). There are two kinds of time series data:
`1.
`Continuous, where we have an observation at every instant of time, e.g. lie
`detectors, electrocardiograms. We denote this using observation X at time t,
`X(t).
`Discrete, where we have an observation at (usually regularly) spaced intervals.
`We denote this as Xt.
`Examples
`
`2.
`
`
`PAGE 2 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`Statistics Glossary - time series data
`
`http://www.stats.gla.ac.uk/steps/glossary/time_series.html
`
`Economics - weekly share prices, monthly profits
`Meteorology - daily rainfall, wind speed, temperature
`Sociology - crime figures (number of arrests, etc), employment figures
`
`Trend Component
`
`We want to increase our understanding of a time series by picking out its main
`features. One of these main features is the trend component. Descriptive techniques
`may be extended to forecast (predict) future values.
`Trend is a long term movement in a time series. It is the underlying direction (an
`upward or downward tendency) and rate of change in a time series, when allowance
`has been made for the other components.
`A simple way of detecting trend in seasonal data is to take averages over a certain
`period. If these averages change with time we can say that there is evidence of a
`trend in the series. There are also more formal tests to enable detection of trend in
`time series.
`It can be helpful to model trend using straight lines, polynomials etc.
`See also time series.
`See also cyclical component.
`See also seasonal component.
`See also irregular component.
`
`Cyclical Component
`
`We want to increase our understanding of a time series by picking out its main
`features. One of these main features is the cyclical component. Descriptive
`techniques may be extended to forecast (predict) future values.
`
`
`PAGE 3 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`Statistics Glossary - time series data
`
`http://www.stats.gla.ac.uk/steps/glossary/time_series.html
`
`In weekly or monthly data, the cyclical component describes any regular fluctuations.
`It is a non-seasonal component which varies in a recognisable cycle.
`See also time series.
`See also trend component.
`See also seasonal component.
`See also irregular component.
`
`Seasonal Component
`
`We want to increase our understanding of a time series by picking out its main
`features. One of these main features is the seasonal component. Descriptive
`techniques may be extended to forecast (predict) future values.
`In weekly or monthly data, the seasonal component, often referred to as seasonality,
`is the component of variation in a time series which is dependent on the time of year.
`It describes any regular fluctuations with a period of less than one year. For example,
`the costs of various types of fruits and vegetables, unemployment figures and
`average daily rainfall, all show marked seasonal variation.
`We are interested in comparing the seasonal effects within the years, from year to
`year; removing seasonal effects so that the time series is easier to cope with; and,
`also interested in adjusting a series for seasonal effects using various models.
`See also time series.
`See also trend component.
`See also cyclical component.
`See also irregular component.
`
`Irregular Component
`
`We want to increase our understanding of a time series by picking out its main
`features. One of these main features is the irregular component (or 'noise').
`Descriptive techniques may be extended to forecast (predict) future values.
`The irregular component is that left over when the other components of the series
`(trend, seasonal and cyclical) have been accounted for.
`See also time series.
`See also trend component.
`See also cyclical component.
`See also seasonal component.
`
`
`PAGE 4 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`Statistics Glossary - time series data
`
`http://www.stats.gla.ac.uk/steps/glossary/time_series.html
`
`Smoothing
`
`Smoothing techniques are used to reduce irregularities (random fluctuations) in time
`series data. They provide a clearer view of the true underlying behaviour of the
`series.
`In some time series, seasonal variation is so strong it obscures any trends or cycles
`which are very important for the understanding of the process being observed.
`Smoothing can remove seasonality and makes long term fluctuations in the series
`stand out more clearly.
`The most common type of smoothing technique is moving average smoothing
`although others do exist. Since the type of seasonality will vary from series to series,
`so must the type of smoothing.
`
`Exponential Smoothing
`
`Exponential smoothing is a smoothing technique used to reduce irregularities
`(random fluctuations) in time series data, thus providing a clearer view of the true
`underlying behaviour of the series. It also provides an effective means of predicting
`future values of the time series (forecasting).
`
`Moving Average Smoothing
`
`A moving average is a form of average which has been adjusted to allow for seasonal
`or cyclical components of a time series. Moving average smoothing is a smoothing
`technique used to make the long term trends of a time series clearer.
`When a variable, like the number of unemployed, or the cost of strawberries, is
`graphed against time, there are likely to be considerable seasonal or cyclical
`components in the variation. These may make it difficult to see the underlying trend.
`These components can be eliminated by taking a suitable moving average.
`By reducing random fluctuations, moving average smoothing makes long term trends
`clearer.
`
`Running Medians Smoothing
`
`Running medians smoothing is a smoothing technique analogous to that used for
`moving averages. The purpose of the technique is the same, to make a trend clearer
`by reducing the effects of other fluctuations.
`
`
`PAGE 5 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
`
`Statistics Glossary - time series data
`
`http://www.stats.gla.ac.uk/steps/glossary/time_series.html
`
`Differencing
`
`Differencing is a popular and effective method of removing trend from a time series.
`This provides a clearer view of the true underlying behaviour of the series.
`
`Autocorrelation
`
`Autocorrelation is the correlation (relationship) between members of a time series of
`observations, such as weekly share prices or interest rates, and the same values at a
`fixed time interval later.
`More technically, autocorrelation occurs when residual error terms from observations
`of the same variable at different times are correlated (related).
`
`Extrapolation
`
`Extrapolation is when the value of a variable is estimated at times which have not yet
`been observed. This estimate may be reasonably reliable for short times into the
`future, but for longer times, the estimate is liable to become less accurate.
`Example
`Suppose Angela was 1.20m tall on January 1st 1975, and 1.40m tall on January 1st
`1976. By extrapolation, it could be estimated that by January 1st 1977 she would
`have grown another 0.20m to be 1.60m tall. This however assumes that she
`continued to grow at the same rate. This must eventually become a false assumption,
`otherwise by January 1st 1980, she would be a giantess.
`
`Top of page | Main Contents page
`
`PAGE 6 OF 6
`
`SONOS EXHIBIT 1018
`IPR of U.S. Pat. No. 8,942,252
`
`
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