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Drift Rate
In probability theory, stochastic drift is the change of the average value of a stochastic (random) process. A related concept is the drift rate, which is the rate at which the average changes. For example, a process that counts the number of heads in a series of n fair coin tosses has a drift rate of 1/2 per toss. This is in contrast to the random fluctuations about this average value. The stochastic mean of that coin-toss process is 1/2 and the drift rate of the stochastic mean is 0, assuming 1 = heads and 0 = tails. Stochastic drifts in population studies Longitudinal studies of secular events are frequently conceptualized as consisting of a trend component fitted by a polynomial, a cyclical component often fitted by an analysis based on autocorrelations or on a Fourier series, and a random component (stochastic drift) to be removed. In the course of the time series analysis, identification of cyclical and stochastic drift components is often attempted by ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Probability Theory
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set of axioms of probability, axioms. Typically these axioms formalise probability in terms of a probability space, which assigns a measure (mathematics), measure taking values between 0 and 1, termed the probability measure, to a set of outcomes called the sample space. Any specified subset of the sample space is called an event (probability theory), event. Central subjects in probability theory include discrete and continuous random variables, probability distributions, and stochastic processes (which provide mathematical abstractions of determinism, non-deterministic or uncertain processes or measured Quantity, quantities that may either be single occurrences or evolve over time in a random fashion). Although it is no ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gross Domestic Product
Gross domestic product (GDP) is a monetary measure of the total market value of all the final goods and services produced and rendered in a specific time period by a country or countries. GDP is often used to measure the economic performance of a country or region. Several national and international economic organizations maintain definitions of GDP, such as the OECD and the International Monetary Fund. GDP is often used as a metric for international comparisons as well as a broad measure of economic progress. It is often considered to be the world's most powerful statistical indicator of national development and progress. The GDP can be divided by the total population to obtain the average GDP per capita. Total GDP can also be broken down into the contribution of each industry or sector of the economy. Nominal GDP is useful when comparing national economies on the international market according to the exchange rate. To compare economies over time inflation can be adjus ... [...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] |
Secular Variation
The secular variation of a time series is its long-term, non-periodic variation (see '' Decomposition of time series''). Whether a variation is perceived as secular or not depends on the available timescale: a variation that is secular over a timescale of centuries may be a segment of what is, over a timescale of millions of years, a periodic variation. Natural quantities often have both periodic and secular variations. Secular variation is sometimes called secular trend or secular drift when the emphasis is on a linear long-term trend. The term is used wherever time series are applicable in history, economics, operations research, biological anthropology, and astronomy (particularly celestial mechanics) such as VSOP (planets). Etymology The word ''secular'', from the Latin root ''saecularis'' ("of an age, occurring once in an age"), has two basic meanings: I. Of or pertaining to the world (from which secularity is derived), and II. Of or belonging to an age or long period. T ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Expected Value
In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, expectation value, or first Moment (mathematics), moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean, mean of the possible values a random variable can take, weighted by the probability of those outcomes. Since it is obtained through arithmetic, the expected value sometimes may not even be included in the sample data set; it is not the value you would expect to get in reality. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by Integral, integration. In the axiomatic foundation for probability provided by measure theory, the expectation is given by Lebesgue integration. The expected value of a random variable is often denoted by , , or , with a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Price Level
The general price level is a hypothetical measure of overall prices for some set of goods and services (the consumer basket), in an economy or monetary union during a given interval (generally one day), normalized relative to some base set. Typically, the general price level is approximated with a daily price ''index'', normally the Daily CPI. The general price level can change more than once per day during hyperinflation. Theoretical foundation The classical dichotomy is the assumption that there is a relatively clean distinction between overall increases or decreases in prices and underlying, “nominal” economic variables. Thus, if prices ''overall'' increase or decrease, it is assumed that this change can be decomposed as follows: Given a set C of goods and services, the total value of transactions in C at time t is :\sum_ (p_\cdot q_)=\sum_ P_t\cdot p'_)\cdot q_P_t\cdot \sum_ (p'_\cdot q_) where :q_\, represents the quantity of c at time t :p_\, represents the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monetary Policy
Monetary policy is the policy adopted by the monetary authority of a nation to affect monetary and other financial conditions to accomplish broader objectives like high employment and price stability (normally interpreted as a low and stable rate of inflation). Further purposes of a monetary policy may be to contribute to economic stability or to maintain predictable exchange rates with other currencies. Today most central banks in developed countries conduct their monetary policy within an inflation targeting framework, whereas the monetary policies of most developing countries' central banks target some kind of a fixed exchange rate system. A third monetary policy strategy, targeting the money supply, was widely followed during the 1980s, but has diminished in popularity since then, though it is still the official strategy in a number of emerging economies. The tools of monetary policy vary from central bank to central bank, depending on the country's stage of development, inst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
First Difference
In mathematics, a recurrence relation is an equation according to which the nth term of a sequence of numbers is equal to some combination of the previous terms. Often, only k previous terms of the sequence appear in the equation, for a parameter k that is independent of n; this number k is called the ''order'' of the relation. If the values of the first k numbers in the sequence have been given, the rest of the sequence can be calculated by repeatedly applying the equation. In ''linear recurrences'', the th term is equated to a linear function of the k previous terms. A famous example is the recurrence for the Fibonacci numbers, F_n=F_+F_ where the order k is two and the linear function merely adds the two previous terms. This example is a linear recurrence with constant coefficients, because the coefficients of the linear function (1 and 1) are constants that do not depend on n. For these recurrences, one can express the general term of the sequence as a closed-form expression of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Variable
A random variable (also called random quantity, aleatory variable, or stochastic variable) is a Mathematics, mathematical formalization of a quantity or object which depends on randomness, random events. The term 'random variable' in its mathematical definition refers to neither randomness nor variability but instead is a mathematical function (mathematics), function in which * the Domain of a function, domain is the set of possible Outcome (probability), outcomes in a sample space (e.g. the set \ which are the possible upper sides of a flipped coin heads H or tails T as the result from tossing a coin); and * the Range of a function, range is a measurable space (e.g. corresponding to the domain above, the range might be the set \ if say heads H mapped to -1 and T mapped to 1). Typically, the range of a random variable is a subset of the Real number, real numbers. Informally, randomness typically represents some fundamental element of chance, such as in the roll of a dice, d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Root
In probability theory and statistics, a unit root is a feature of some stochastic processes (such as random walks) that can cause problems in statistical inference involving time series models. A linear stochastic process has a unit root if 1 is a root of the process's characteristic equation. Such a process is non-stationary but does not always have a trend. If the other roots of the characteristic equation lie inside the unit circle—that is, have a modulus (absolute value) less than one—then the first difference of the process will be stationary; otherwise, the process will need to be differenced multiple times to become stationary. If there are ''d'' unit roots, the process will have to be differenced ''d'' times in order to make it stationary. Due to this characteristic, unit root processes are also called difference stationary. Unit root processes may sometimes be confused with trend-stationary processes; while they share many properties, they are different in m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Trend-stationary Process
In the statistical analysis of time series, a trend-stationary process is a stochastic process from which an underlying trend (function solely of time) can be removed, leaving a stationary process. The trend does not have to be linear. Conversely, if the process requires differencing to be made stationary, then it is called difference stationary and possesses one or more unit roots. Those two concepts may sometimes be confused, but while they share many properties, they are different in many aspects. It is possible for a time series to be non-stationary, yet have no unit root and be trend-stationary. In both unit root and trend-stationary processes, the mean can be growing or decreasing over time; however, in the presence of a shock, trend-stationary processes are mean-reverting (i.e. transitory, the time series will converge again towards the growing mean, which was not affected by the shock) while unit-root processes have a permanent impact on the mean (i.e. no convergence ove ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stationary Process
In mathematics and statistics, a stationary process (also called a strict/strictly stationary process or strong/strongly stationary process) is a stochastic process whose statistical properties, such as mean and variance, do not change over time. More formally, the joint probability distribution of the process remains the same when shifted in time. This implies that the process is statistically consistent across different time periods. Because many statistical procedures in time series analysis assume stationarity, non-stationary data are frequently transformed to achieve stationarity before analysis. A common cause of non-stationarity is a trend in the mean, which can be due to either a unit root or a deterministic trend. In the case of a unit root, stochastic shocks have permanent effects, and the process is not mean-reverting. With a deterministic trend, the process is called trend-stationary, and shocks have only transitory effects, with the variable tending towards a determin ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
