|
Seasonal Variation
In time series data, seasonality refers to the trends that occur at specific regular intervals less than a year, such as weekly, monthly, or quarterly. Seasonality may be caused by various factors, such as weather, vacation, and holidays and consists of periodic, repetitive, and generally regular and predictable patterns in the levels of a time series. Seasonal fluctuations in a time series can be contrasted with cyclical patterns. The latter occur when the data exhibits rises and falls that are not of a fixed period. Such non-seasonal fluctuations are usually due to economic conditions and are often related to the "business cycle"; their period usually extends beyond a single year, and the fluctuations are usually of at least two years. Organisations facing seasonal variations, such as ice-cream vendors, are often interested in knowing their performance relative to the normal seasonal variation. Seasonal variations in the labour market can be attributed to the entrance of school ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time Series
In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average. A time series is very frequently plotted via a run chart (which is a temporal line chart). Time series are used in statistics, signal processing, pattern recognition, econometrics, mathematical finance, weather forecasting, earthquake prediction, electroencephalography, control engineering, astronomy, communications engineering, and largely in any domain of applied science and engineering which involves temporal measurements. Time series ''analysis'' comprises methods for analyzing time series data in order to extract meaningful statistics and other characteristics of the data. Time series ''f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Additive Model
In statistics, an additive model (AM) is a nonparametric regression method. It was suggested by Jerome H. Friedman and Werner Stuetzle (1981) and is an essential part of the ACE algorithm. The ''AM'' uses a one-dimensional smoother to build a restricted class of nonparametric regression models. Because of this, it is less affected by the curse of dimensionality than a ''p''-dimensional smoother. Furthermore, the ''AM'' is more flexible than a standard linear model, while being more interpretable than a general regression surface at the cost of approximation errors. Problems with ''AM'', like many other machine-learning methods, include model selection, overfitting, and multicollinearity. Description Given a data set \_^n of ''n'' statistical units, where \_^n represent predictors and y_i is the outcome, the ''additive model'' takes the form : \mathrm x_, \ldots, x_= \beta_0+\sum_^p f_j(x_) or : Y= \beta_0+\sum_^p f_j(X_)+\varepsilon Where \mathrm \epsilon = 0, \mathrm(\e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Season
A season is a division of the year based on changes in weather, ecology, and the number of daylight hours in a given region. On Earth, seasons are the result of the axial parallelism of Earth's axial tilt, tilted orbit around the Sun. In temperate and polar regions, the seasons are marked by changes in the intensity of sunlight that reaches the Earth's surface, variations of which may cause animals to undergo hibernation or to Migration (ecology), migrate, and plants to be dormant. Various cultures define the number and nature of seasons based on regional variations, and as such there are a number of both modern and historical definitions of the seasons. The Northern Hemisphere experiences most direct sunlight during May, June, and July (thus the traditional celebration of Midsummer in June), as the hemisphere faces the Sun. For the Southern Hemisphere it is instead in November, December, and January. It is Earth's axial tilt that causes the Sun to be higher in the sky during the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dummy Variable (statistics)
In regression analysis, a dummy variable (also known as indicator variable or just dummy) is one that takes a binary value (0 or 1) to indicate the absence or presence of some categorical effect that may be expected to shift the outcome. For example, if we were studying the relationship between biological sex and income, we could use a dummy variable to represent the sex of each individual in the study. The variable could take on a value of 1 for males and 0 for females (or vice versa). In machine learning this is known as one-hot encoding. Dummy variables are commonly used in regression analysis to represent categorical variables that have more than two levels, such as education level or occupation. In this case, multiple dummy variables would be created to represent each level of the variable, and only one dummy variable would take on a value of 1 for each observation. Dummy variables are useful because they allow us to include categorical variables in our analysis, which ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Independent Variable
A variable is considered dependent if it depends on (or is hypothesized to depend on) an independent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by a mathematical function), on the values of other variables. Independent variables, on the other hand, are not seen as depending on any other variable in the scope of the experiment in question. Rather, they are controlled by the experimenter. In pure mathematics In mathematics, a function is a rule for taking an input (in the simplest case, a number or set of numbers)Carlson, Robert. A concrete introduction to real analysis. CRC Press, 2006. p.183 and providing an output (which may also be a number). A symbol that stands for an arbitrary input is called an independent variable, while a symbol that stands for an arbitrary output is called a dependent variable. The most common symbol for the input is , and the most common symbol for the output is ; the function ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ordinary Least Squares
In statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression In statistics, linear regression is a statistical model, model that estimates the relationship between a Scalar (mathematics), scalar response (dependent variable) and one or more explanatory variables (regressor or independent variable). A mode ... model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable. Some sources consider OLS to be linear regression. Geometrically, this is seen as the sum of the squared distances, parallel to the axis of the dependent variable, between each data point in the set and the corresponding point on the regression ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
X-12-ARIMA
X-13ARIMA-SEATS, successor to X-12-ARIMA and X-11, is a set of statistical methods for seasonal adjustment and other descriptive analysis of time series data that are implemented in the U.S. Census Bureau's software package. These methods are or have been used by Statistics Canada, Australian Bureau of Statistics, and the statistical offices of many other countries. X-12-ARIMA can be used together with many statistical packages, such as SAS in its econometric and time series (ETS) package, R in its (seasonal) package, Gretl or EViews which provides a graphical user interface for X-12-ARIMA, and NumXL which avails X-12-ARIMA functionality in Microsoft Excel. There is also a version for MATLAB. Notable statistical agencies presently using X-12-ARIMA for seasonal adjustment include Statistics Canada, the U.S. Bureau of Labor Statistics and Census and Statistics Department (Hong Kong). The Brazilian Institute of Geography and Statistics uses X-13-ARIMA. X-12-ARIMA was the succes ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Decomposition Of Time Series
The decomposition of time series is a statistical task that deconstructs a time series into several components, each representing one of the underlying categories of patterns. There are two principal types of decomposition, which are outlined below. Decomposition based on rates of change This is an important technique for all types of time series analysis, especially for seasonal adjustment. It seeks to construct, from an observed time series, a number of component series (that could be used to reconstruct the original by additions or multiplications) where each of these has a certain characteristic or type of behavior. For example, time series are usually decomposed into: *T_t, the trend component at time ''t'', which reflects the long-term progression of the series ( secular variation). A trend exists when there is a persistent increasing or decreasing direction in the data. The trend component does not have to be linear. *C_t, the cyclical component at time ''t'', which refl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cyclostationary Process
A cyclostationary process is a signal having statistical properties that vary cyclically with time. A cyclostationary process can be viewed as multiple interleaved stationary processes. For example, the maximum daily temperature in New York City can be modeled as a cyclostationary process: the maximum temperature on July 21 is statistically different from the temperature on December 20; however, it is a reasonable approximation that the temperature on December 20 of different years has identical statistics. Thus, we can view the random process composed of daily maximum temperatures as 365 interleaved stationary processes, each of which takes on a new value once per year. Definition There are two differing approaches to the treatment of cyclostationary processes. The stochastic approach is to view measurements as an instance of an abstract stochastic process model. As an alternative, the more empirical approach is to view the measurements as a single time series of data—that wh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ARIMA
Arima, officially The Royal Chartered Borough of Arima is the easternmost and second largest in area of the three boroughs of Trinidad and Tobago. It is geographically adjacent to Sangre Grande and Arouca at the south central foothills of the Northern Range. To the south is the Caroni–Arena Dam. Coterminous with Town of Arima since 1888, the borough of Arima is the fourth-largest municipality in population in the country (after Port of Spain, Chaguanas and San Fernando). The census estimated it had 33,606 residents in 2011. In 1887, the town petitioned Queen Victoria for municipal status as part of the celebration for the Golden Jubilee of Queen Victoria. This was granted in the following year, and Arima became a Royal Borough on 1 August 1888. Historically the third-largest town of Trinidad and Tobago, Arima is fourth since Chaguanas became the largest town in the country. History Contrary to the belief that the city is named after the Arawak word for "water", roote ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
