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59-531: The film was in theaters from November 14, 2003, to December 21, 2003. As of July 1, 2008 it had earned over $ 7.8 million, making it the 21st-highest-grossing documentary film in the United States - (in nominal dollars, from 1982 to the present). The film was nominated for the Academy Award for Best Documentary Feature at the 77th Academy Awards . Tupac details his childhood, from growing up with

118-596: A function among a well-defined class that closely matches ("approximates") a target function in a task-specific way. One can distinguish two major classes of function approximation problems: First, for known target functions, approximation theory is the branch of numerical analysis that investigates how certain known functions (for example, special functions ) can be approximated by a specific class of functions (for example, polynomials or rational functions ) that often have desirable properties (inexpensive computation, continuity, integral and limit values, etc.). Second,

177-472: A causal effect on the observed series): the distinction from the multivariate case is that the forcing series may be deterministic or under the experimenter's control. For these models, the acronyms are extended with a final "X" for "exogenous". Non-linear dependence of the level of a series on previous data points is of interest, partly because of the possibility of producing a chaotic time series. However, more importantly, empirical investigations can indicate

236-448: A certain point in time. An equivalent effect may be achieved in the time domain, as in a Kalman filter ; see filtering and smoothing for more techniques. Other related techniques include: Curve fitting is the process of constructing a curve , or mathematical function , that has the best fit to a series of data points, possibly subject to constraints. Curve fitting can involve either interpolation , where an exact fit to

295-571: A certain structure which can be described using a small number of parameters (for example, using an autoregressive or moving-average model ). In these approaches, the task is to estimate the parameters of the model that describes the stochastic process. By contrast, non-parametric approaches explicitly estimate the covariance or the spectrum of the process without assuming that the process has any particular structure. Methods of time series analysis may also be divided into linear and non-linear , and univariate and multivariate . A time series

354-451: A commodity bundle tends to change over time. In contrast, by definition, the real value of the commodity bundle in aggregate remains the same over time. The real values of individual goods or commodities may rise or fall against each other, in relative terms, but a representative commodity bundle as a whole retains its real value as a constant from one period to the next. Real values can for example be expressed in constant 1992 dollars , with

413-418: A function where no data are available, and to summarize the relationships among two or more variables. Extrapolation refers to the use of a fitted curve beyond the range of the observed data, and is subject to a degree of uncertainty since it may reflect the method used to construct the curve as much as it reflects the observed data. For processes that are expected to generally grow in magnitude one of

472-584: A given period will be expressed as deriving in some way from past values, rather than from future values (see time reversibility ). Time series analysis can be applied to real-valued , continuous data, discrete numeric data, or discrete symbolic data (i.e. sequences of characters, such as letters and words in the English language ). Methods for time series analysis may be divided into two classes: frequency-domain methods and time-domain methods. The former include spectral analysis and wavelet analysis ;

531-475: A given time series, attempting to illustrate time dependence at multiple scales. See also Markov switching multifractal (MSMF) techniques for modeling volatility evolution. A hidden Markov model (HMM) is a statistical Markov model in which the system being modeled is assumed to be a Markov process with unobserved (hidden) states. An HMM can be considered as the simplest dynamic Bayesian network . HMM models are widely used in speech recognition , for translating

590-450: A means of transferring knowledge about a sample of a population to the whole population, and to other related populations, which is not necessarily the same as prediction over time. When information is transferred across time, often to specific points in time, the process is known as forecasting . Assigning time series pattern to a specific category, for example identify a word based on series of hand movements in sign language . Splitting

649-508: A mother addicted to crack to being taken care of by drug dealers on the streets, as well as the type of jobs he had to do to get money. He also talks about his love for poetry, his friendship with Jada, what his lyrics mean, and about the negative resentment the media has had on him. This documentary then details his shooting, his reaction to getting shot, his paranoia after getting shot, and ultimately his death. The documentary ends with Tupac coming to terms with his life and his past, understanding

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708-474: A regular time series is manually with a line chart . The datagraphic shows tuberculosis deaths in the United States, along with the yearly change and the percentage change from year to year. The total number of deaths declined in every year until the mid-1980s, after which there were occasional increases, often proportionately - but not absolutely - quite large. A study of corporate data analysts found two challenges to exploratory time series analysis: discovering

767-423: A similar way. For example, the total value of a good produced in a region of a country depends on both the amount and the price. To compare the output of different regions, the nominal output in a region can be adjusted by repricing the goods at common or average prices. Time series In mathematics , a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly,

826-418: A single series. Time series data have a natural temporal ordering. This makes time series analysis distinct from cross-sectional studies , in which there is no natural ordering of the observations (e.g. explaining people's wages by reference to their respective education levels, where the individuals' data could be entered in any order). Time series analysis is also distinct from spatial data analysis where

885-963: 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

944-406: A time series of spoken words into text. Many of these models are collected in the python package sktime . A number of different notations are in use for time-series analysis. A common notation specifying a time series X that is indexed by the natural numbers is written Another common notation is where T is the index set . There are two sets of conditions under which much of the theory

1003-418: A time-series into a sequence of segments. It is often the case that a time-series can be represented as a sequence of individual segments, each with its own characteristic properties. For example, the audio signal from a conference call can be partitioned into pieces corresponding to the times during which each person was speaking. In time-series segmentation, the goal is to identify the segment boundary points in

1062-416: A unified treatment in statistical learning theory , where they are viewed as supervised learning problems. In statistics , prediction is a part of statistical inference . One particular approach to such inference is known as predictive inference , but the prediction can be undertaken within any of the several approaches to statistical inference. Indeed, one description of statistics is that it provides

1121-490: Is a financial asset , g t {\displaystyle g_{t}} is a nominal interest rate and r t {\displaystyle r_{t}} is the corresponding real interest rate ; the first-order approximation r t = g t − i t {\displaystyle r_{t}=g_{t}-i_{t}} is known as the Fisher equation . Looking back into

1180-438: Is a sample of goods , which is used to represent the sum total of goods across the economy to which the goods belong, for the purpose of comparison across different times (or locations). At a single point of time, a commodity bundle consists of a list of goods, and each good in the list has a market price and a quantity. The market value of the good is the market price times the quantity at that point of time. The nominal value of

1239-482: Is a time series data set candidate. If determining a unique record requires a time data field and an additional identifier which is unrelated to time (e.g. student ID, stock symbol, country code), then it is panel data candidate. If the differentiation lies on the non-time identifier, then the data set is a cross-sectional data set candidate. There are several types of motivation and data analysis available for time series which are appropriate for different purposes. In

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1298-419: Is built: Ergodicity implies stationarity, but the converse is not necessarily the case. Stationarity is usually classified into strict stationarity and wide-sense or second-order stationarity . Both models and applications can be developed under each of these conditions, although the models in the latter case might be considered as only partly specified. In addition, time-series analysis can be applied where

1357-459: Is calculated relative to a base or reference date. P 0 {\displaystyle P_{0}} is the value of the index at the base date. For example, if the base date is (the end of) 1992, P 0 {\displaystyle P_{0}} is the value of the index at (the end of) 1992. The price index is typically normalized to start at 100 at the base date, so P 0 {\displaystyle P_{0}}

1416-416: Is closely related to interpolation is the approximation of a complicated function by a simple function (also called regression ). The main difference between regression and interpolation is that polynomial regression gives a single polynomial that models the entire data set. Spline interpolation, however, yield a piecewise continuous function composed of many polynomials to model the data set. Extrapolation

1475-479: Is considered and measured against the actual goods or services for which it can be exchanged at a given time. Real value takes into account inflation and the value of an asset in relation to its purchasing power . In macroeconomics, the real gross domestic product compensates for inflation so economists can exclude inflation from growth figures, and see how much an economy actually grows. Nominal GDP would include inflation, and thus be higher. A commodity bundle

1534-400: Is one type of panel data . Panel data is the general class, a multidimensional data set, whereas a time series data set is a one-dimensional panel (as is a cross-sectional dataset ). A data set may exhibit characteristics of both panel data and time series data. One way to tell is to ask what makes one data record unique from the other records. If the answer is the time data field, then this

1593-441: Is set to 100. The length of time between each value of t {\displaystyle t} and the next one, is normally constant regular time interval, such as a calendar year. P t {\displaystyle P_{t}} is the value of the price index at time t {\displaystyle t} after the base date. P t {\displaystyle P_{t}} equals 100 times

1652-411: Is the change in the price index divided by the price index value at time t − 1 {\displaystyle t-1} : i t = P t − P t − 1 P t − 1 {\displaystyle i_{t}={\frac {P_{t}-P_{t-1}}{P_{t-1}}}} expressed as a percentage. The nominal value of

1711-553: Is the inflation rate. For values of i t {\displaystyle i_{t}} between −1 and 1 (i.e. ±100 percent), we have the Taylor series so Hence as a first-order ( i.e. linear) approximation, The bundle of goods used to measure the Consumer Price Index (CPI) is applicable to consumers. So for wage earners as consumers, an appropriate way to measure real wages (the buying power of wages)

1770-406: Is the process of estimating, beyond the original observation range, the value of a variable on the basis of its relationship with another variable. It is similar to interpolation , which produces estimates between known observations, but extrapolation is subject to greater uncertainty and a higher risk of producing meaningless results. In general, a function approximation problem asks us to select

1829-456: Is to divide the nominal wage (after-tax) by the growth factor in the CPI. Gross domestic product (GDP) is a measure of aggregate output. Nominal GDP in a particular period reflects prices that were current at the time, whereas real GDP compensates for inflation. Price indices and the U.S. National Income and Product Accounts are constructed from bundles of commodities and their respective prices. In

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1888-450: The codomain (range or target set) of g is a finite set, one is dealing with a classification problem instead. A related problem of online time series approximation is to summarize the data in one-pass and construct an approximate representation that can support a variety of time series queries with bounds on worst-case error. To some extent, the different problems ( regression , classification , fitness approximation ) have received

1947-479: The advantage of using predictions derived from non-linear models, over those from linear models, as for example in nonlinear autoregressive exogenous models . Further references on nonlinear time series analysis: (Kantz and Schreiber), and (Abarbanel) Among other types of non-linear time series models, there are models to represent the changes of variance over time ( heteroskedasticity ). These models represent autoregressive conditional heteroskedasticity (ARCH) and

2006-483: The available information ("reading between the lines"). Interpolation is useful where the data surrounding the missing data is available and its trend, seasonality, and longer-term cycles are known. This is often done by using a related series known for all relevant dates. Alternatively polynomial interpolation or spline interpolation is used where piecewise polynomial functions are fitted in time intervals such that they fit smoothly together. A different problem which

2065-413: The base year are respectively: The real wage each year measures the buying power of the hourly wage in common terms. In this example, the real wage rate increased by 20 percent, meaning that an hour's wage would buy 20% more goods in year 2 compared with year 1. As was shown in the section above on the real growth rate, where and as a first-order approximation, In the case where the growing quantity

2124-448: The case of GDP, a suitable price index is the GDP price index. In the U.S. National Income and Product Accounts, nominal GDP is called GDP in current dollars (that is, in prices current for each designated year), and real GDP is called GDP in [base-year] dollars (that is, in dollars that can purchase the same quantity of commodities as in the base year). then real wages using year 1 as

2183-668: The collection comprises a wide variety of representation ( GARCH , TARCH, EGARCH, FIGARCH, CGARCH, etc.). Here changes in variability are related to, or predicted by, recent past values of the observed series. This is in contrast to other possible representations of locally varying variability, where the variability might be modelled as being driven by a separate time-varying process, as in a doubly stochastic model . In recent work on model-free analyses, wavelet transform based methods (for example locally stationary wavelets and wavelet decomposed neural networks) have gained favor. Multiscale (often referred to as multiresolution) techniques decompose

2242-552: The commodity bundle at a point of time is the total market value of the commodity bundle, depending on the market price, and the quantity, of each good in the commodity bundle which are current at the time. A price index is the relative price of a commodity bundle. A price index can be measured over time, or at different locations or markets. If it is measured over time, it is a series of values P t {\displaystyle P_{t}} over time t {\displaystyle t} . A time series price index

2301-556: The context of statistics , econometrics , quantitative finance , seismology , meteorology , and geophysics the primary goal of time series analysis is forecasting . In the context of signal processing , control engineering and communication engineering it is used for signal detection. Other applications are in data mining , pattern recognition and machine learning , where time series analysis can be used for clustering , classification , query by content, anomaly detection as well as forecasting . A simple way to examine

2360-421: The curves in the graphic (and many others) can be fitted by estimating their parameters. The construction of economic time series involves the estimation of some components for some dates by interpolation between values ("benchmarks") for earlier and later dates. Interpolation is estimation of an unknown quantity between two known quantities (historical data), or drawing conclusions about missing information from

2419-402: The data is required, or smoothing , in which a "smooth" function is constructed that approximately fits the data. A related topic is regression analysis , which focuses more on questions of statistical inference such as how much uncertainty is present in a curve that is fit to data observed with random errors. Fitted curves can be used as an aid for data visualization, to infer values of

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2478-470: The data. Time series forecasting is the use of a model to predict future values based on previously observed values. Generally, time series data is modelled as a stochastic process . While regression analysis is often employed in such a way as to test relationships between one or more different time series, this type of analysis is not usually called "time series analysis", which refers in particular to relationships between different points in time within

2537-427: The director's loyalty lies in this one-sided tribute; however, Tupac's charisma makes this doc an engaging sit". Metacritic assigned the film a weighted average score of 66 out of 100, based on 33 critics, indicating "generally favorable reviews". 2005 : Academy Award for Best Documentary Feature (nomination) An official 14-track soundtrack album was released, although it only contained nine songs that featured in

2596-552: The feature extraction using chunking with sliding windows. It was found that the cluster centers (the average of the time series in a cluster - also a time series) follow an arbitrarily shifted sine pattern (regardless of the dataset, even on realizations of a random walk ). This means that the found cluster centers are non-descriptive for the dataset because the cluster centers are always nonrepresentative sine waves. Models for time series data can have many forms and represent different stochastic processes . When modeling variations in

2655-484: The former three. Extensions of these classes to deal with vector-valued data are available under the heading of multivariate time-series models and sometimes the preceding acronyms are extended by including an initial "V" for "vector", as in VAR for vector autoregression . An additional set of extensions of these models is available for use where the observed time-series is driven by some "forcing" time-series (which may not have

2714-492: The growth factor of the price index. Real values can be found by dividing the nominal value by the growth factor of a price index. Using the price index growth factor as a divisor for converting a nominal value into a real value, the real value at time t relative to the base date is: The real growth rate r t {\displaystyle r_{t}} is the change in a nominal quantity Q t {\displaystyle Q_{t}} in real terms since

2773-446: The latter include auto-correlation and cross-correlation analysis. In the time domain, correlation and analysis can be made in a filter-like manner using scaled correlation , thereby mitigating the need to operate in the frequency domain. Additionally, time series analysis techniques may be divided into parametric and non-parametric methods. The parametric approaches assume that the underlying stationary stochastic process has

2832-465: The level of a process, three broad classes of practical importance are the autoregressive (AR) models, the integrated (I) models, and the moving-average (MA) models. These three classes depend linearly on previous data points. Combinations of these ideas produce autoregressive moving-average (ARMA) and autoregressive integrated moving-average (ARIMA) models. The autoregressive fractionally integrated moving-average (ARFIMA) model generalizes

2891-433: The movie. The following tracks, listed alphabetically by title, are written and/or performed by Tupac and feature in the film: The following tracks, which Tupac had no input on, are also featured in the film: Shipments figures based on certification alone. Real versus nominal value (economics) In economics , nominal value refers to value measured in terms of absolute money amounts, whereas real value

2950-451: The observations typically relate to geographical locations (e.g. accounting for house prices by the location as well as the intrinsic characteristics of the houses). A stochastic model for a time series will generally reflect the fact that observations close together in time will be more closely related than observations further apart. In addition, time series models will often make use of the natural one-way ordering of time so that values for

3009-417: The past, the ex post real interest rate is approximately the historical nominal interest rate minus inflation. Looking forward into the future, the expected real interest rate is approximately the nominal interest rate minus the expected inflation rate. Not only time-series data, as above, but also cross-sectional data which depends on prices which may vary geographically for example, can be adjusted in

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3068-399: The previous date t − 1 {\displaystyle t-1} . It measures by how much the buying power of the quantity has changed over a single period. where g t {\displaystyle g_{t}} is the nominal growth rate of Q t {\displaystyle Q_{t}} , and i t {\displaystyle i_{t}}

3127-459: The price level fixed 100 at the base date. The price index is applied to adjust the nominal value Q {\displaystyle Q} of a quantity, such as wages or total production, to obtain its real value. The real value is the value expressed in terms of purchasing power in the base year. The index price divided by its base-year value P t / P 0 {\displaystyle P_{t}/P_{0}} gives

3186-573: The series are seasonally stationary or non-stationary. Situations where the amplitudes of frequency components change with time can be dealt with in time-frequency analysis which makes use of a time–frequency representation of a time-series or signal. Tools for investigating time-series data include: Time-series metrics or features that can be used for time series classification or regression analysis : Time series can be visualized with two categories of chart: Overlapping Charts and Separated Charts. Overlapping Charts display all-time series on

3245-644: The shape of interesting patterns, and finding an explanation for these patterns. Visual tools that represent time series data as heat map matrices can help overcome these challenges. This approach may be based on harmonic analysis and filtering of signals in the frequency domain using the Fourier transform , and spectral density estimation . Its development was significantly accelerated during World War II by mathematician Norbert Wiener , electrical engineers Rudolf E. Kálmán , Dennis Gabor and others for filtering signals from noise and predicting signal values at

3304-454: The target function, call it g , may be unknown; instead of an explicit formula, only a set of points (a time series) of the form ( x , g ( x )) is provided. Depending on the structure of the domain and codomain of g , several techniques for approximating g may be applicable. For example, if g is an operation on the real numbers , techniques of interpolation , extrapolation , regression analysis , and curve fitting can be used. If

3363-499: The time-series, and to characterize the dynamical properties associated with each segment. One can approach this problem using change-point detection , or by modeling the time-series as a more sophisticated system, such as a Markov jump linear system. Time series data may be clustered, however special care has to be taken when considering subsequence clustering. Time series clustering may be split into Subsequence time series clustering resulted in unstable (random) clusters induced by

3422-493: The value of the commodity bundle at time t {\displaystyle t} , divided by the value of the commodity bundle at the base date. If the price of the commodity bundle has increased by one percent over the first period after the base date, then P 1 = 101. The inflation rate i t {\displaystyle i_{t}} between time t − 1 {\displaystyle t-1} and time t {\displaystyle t}

3481-453: The wrongs that he has done, as well as giving a monologue about stereotypes of Black men, telling Blacks to not give in to stereotypes and to control themselves, and it also shows the impact Tupac has had on the entire world. Tupac: Resurrection has an approval rating of 78% on review aggregator website Rotten Tomatoes , based on 90 reviews, and an average rating of 6.75/10. The website's critical consensus states, "There's no question where

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