scholarly journals TFR Predictions Based on Brownian Motion Theory

2002 ◽  
pp. 207-219
Author(s):  
Keilman Nico
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Random Walk ◽  
Predictive Distribution ◽  
Major Effect ◽  
Common Time ◽  
Population Forecasts ◽  
Sample Paths ◽  
Long Run ◽  
Future Fertility

In stochastic population forecasts, the predictive distribution of the TFR is of centralconcern. Common time series models can be used to predict the TFR and itsmoments on the short run (up to 10 or 20 years), but on the long run (40-50 years)they result in excessively wide prediction intervals. The aim of this study is toanalyse and apply a time series model for the TFR, which restricts the predictedvalues to a certain pre-specified interval.I will model the time series of log TFR-values as a Brownian motion with absorbingupper barrier. I will give and analyse expressions for the predictive distribution of the log of the TFR assuming itfollows a Brownian motion with absorbing ceiling; expressions for the first and second moments of the predictive distribution ofthe log of the TFR.When the log of the TFR follows a random walk with absorbing ceiling, I find thatthe second moment of the predictive distribution for the long-run TFR in Norwayis insensitive for ceiling levels beyond a threshold of approximately 3.4 childrenper woman. This conclusion holds for a fairly broad range of innovation variances.If the log of the TFR follows a random walk, sample paths that exceed approximately3.4 children per woman may be rejected when simulating future fertility in Westerncountries. This will not have any major effect on the width of the long-termpredictive distribution.

scholarly journals Evaluating probabilistic population forecasts

2020 ◽  
Author(s):  
Nico Keilman
Keyword(s):  
The Netherlands ◽  
Oldest Old ◽  
Predictive Distribution ◽  
Scoring Rules ◽  
The European Union ◽  
Population Forecast ◽  
Population Forecasts ◽  
Sample Paths ◽  
Population Forecasting ◽  
And Migration

Abstract We demonstrate how a probabilistic population forecast can be evaluated, when observations for the predicted variables become available. Statisticians have developed various scoring rules for that purpose, but there are hardly any applications in population forecasting literature. A scoring rule measures the distance between the probability distribution of the predicted variable, and the actual outcome. We use scoring rules that reward accuracy (the outcome is close to the expected value of the prediction) and sharpness (the predictive distribution has low variance, which makes it difficult to hit the target).We evaluate probabilistic population forecasts for France, the Netherlands, and Norway. For all three countries, we use results from the UPE-project ("Uncertain Population of Europe"). We inspect prediction intervals for population size in the period 2004-2019 and 3000 sample paths for population pyramids for the year 2010. For the Netherlands and for Norway, we compare the UPE-results with findings from the official probabilistic population forecast by Statistics Netherlands (2001-2019) and from a probabilistic forecast for Norway (1997-2019). All forecasts were computed using the cohort-component method and stochastically varying parameters for fertility, mortality and migration. We show that the UPE-forecasts for the Netherlands and for Norway performed better than the other forecasts for these two countries. The error in the jump-off population caused a bad score for the French forecast.We evaluate the 3000 UPE-simulations of the age and sex composition predicted for the year 2010. When normalized for population numbers in each age-sex category, the predictions for the Netherlands received the best scores, except for the oldest old. The age pattern for the Norwegian score reflects the under-prediction of immigration after the enlargement of the European Union in 2005.

Stochastic motions on the 3-sphere governed by wave and heat equations

1987 ◽  
Vol 24 (02) ◽  
pp. 315-327
Author(s):  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Maxwell Equations ◽  
Telegraph Equation ◽  
Random Motion ◽  
Heat Equations ◽  
Spherical Coordinates ◽  
Sample Paths

In this paper a random motion on the surface of the 3-sphere whose probability law is a solution of the telegraph equation in spherical coordinates is presented. The connection of equations governing the random motion with Maxwell equations is examined together with some qualitative features of its sample paths. Finally Brownian motion on the 3-sphere is derived as the limiting process of a random walk with latitude-changing probabilities.

Stochastic motions on the 3-sphere governed by wave and heat equations

1987 ◽  
Vol 24 (2) ◽  
pp. 315-327 ◽  
Author(s):  
Enzo Orsingher
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Maxwell Equations ◽  
Telegraph Equation ◽  
Random Motion ◽  
Heat Equations ◽  
Spherical Coordinates ◽  
Sample Paths

In this paper a random motion on the surface of the 3-sphere whose probability law is a solution of the telegraph equation in spherical coordinates is presented. The connection of equations governing the random motion with Maxwell equations is examined together with some qualitative features of its sample paths. Finally Brownian motion on the 3-sphere is derived as the limiting process of a random walk with latitude-changing probabilities.

scholarly journals A Wavelet-Based Almost-Sure Uniform Approximation of Fractional Brownian Motion with a Parallel Algorithm

2014 ◽  
Vol 51 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Dawei Hong ◽  
Shushuang Man ◽  
Jean-Camille Birget ◽  
Desmond S. Lun
Keyword(s):  
Brownian Motion ◽  
Convergence Rate ◽  
Fractional Brownian Motion ◽  
Parallel Algorithm ◽  
Uniform Approximation ◽  
Haar Wavelets ◽  
Hurst Index ◽  
Sample Paths ◽  
Vanishing Moment ◽  
Uniform Expansion

We construct a wavelet-based almost-sure uniform approximation of fractional Brownian motion (FBM) (Bt(H))_t∈[0,1] of Hurst index H ∈ (0, 1). Our results show that, by Haar wavelets which merely have one vanishing moment, an almost-sure uniform expansion of FBM for H ∈ (0, 1) can be established. The convergence rate of our approximation is derived. We also describe a parallel algorithm that generates sample paths of an FBM efficiently.

LEARNING DYNAMICS AND NONLINEAR MISSPECIFICATION IN AN ARTIFICIAL FINANCIAL MARKET

2009 ◽  
Vol 13 (5) ◽  
pp. 625-655 ◽  
Author(s):  
Christophre Georges ◽  
John C. Wallace
Keyword(s):  
Time Series ◽  
Financial Market ◽  
Consistency Condition ◽  
Nonlinear Structure ◽  
State Variable ◽  
Bounded Memory ◽  
Long Run ◽  
Finite Memory ◽  
Aggregate Dynamics ◽  
True Structure

In this paper, we explore the consequence of learning to forecast in a very simple environment. Agents have bounded memory and incorrectly believe that there is nonlinear structure underlying the aggregate time series dynamics. Under social learning with finite memory, agents may be unable to learn the true structure of the economy and rather may chase spurious trends, destabilizing the actual aggregate dynamics. We explore the degree to which agents' forecasts are drawn toward a minimal state variable learning equilibrium as well as a weaker long-run consistency condition.

Self-avoiding random walk: A Brownian motion model with local time drift

1987 ◽  
Vol 74 (2) ◽  
pp. 271-287 ◽  
Author(s):  
J. R. Norris ◽  
L. C. G. Rogers ◽  
David Williams
Keyword(s):  
Brownian Motion ◽  
Random Walk ◽  
Local Time ◽  
Motion Model ◽  
Time Drift ◽  
Brownian Motion Model

Forecasting Long-Run Coal Price in China: A Shifting Trend Time-Series Approach

2010 ◽  
Vol 14 (3) ◽  
pp. 499-519 ◽  
Author(s):  
Baomin Dong ◽  
Xuefeng Li ◽  
Boqiang Lin
Keyword(s):  
Time Series ◽  
Coal Price ◽  
Long Run ◽  
Time Series Approach

The Impact of Terms of Trade on the Export Structure of Manufactured Products in Different Economic Developing Status

2021 ◽  
Vol 1 (1) ◽  
pp. 59-67
Author(s):  
Kai-Ting Huang ◽  
Keyword(s):  
Time Series ◽  
Terms Of Trade ◽  
Development Status ◽  
Structural Time Series ◽  
Export Structure ◽  
Primary Products ◽  
Long Run ◽  
Deterministic Trend ◽  
Manufactured Products ◽  
The Impact

The Prebisch-Singer Hypothesis states that in structural time series analysis, the terms of trade between primary products and manufacturers have a negative deterministic trend. Many researchers argued that the deterioration in trade is the type of country in which the products are exported, regardless of whether the types of products exported by such countries are primary or manufactured products. This paper employs a development-differentiated model to analyze the correlation between various terms of trade and the export proportion of manufactured products on different economies of development status. In the long run, stable co-integration relations exist between terms of trade and the export proportion of manufactured products for development status. Furthermore, the increased proportion of manufactured products exports is the Granger casualty for the worse terms of trade for several economies of development status. The results demonstrated that changing the terms of trade is significantly influenced by structured changes in the export proportion of manufactured products for the development status of economies.

scholarly journals Some Applications of Lévy Processes to Stochastic Investment Models for Actuarial Use

1998 ◽  
Vol 28 (1) ◽  
pp. 77-93 ◽  
Author(s):  
Terence Chan
Keyword(s):  
Time Series ◽  
Brownian Motion ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Differential Equations ◽  
Continuous Time ◽  
Investment Model ◽  
Stable Processes ◽  
Gamma Processes ◽  
Investment Models

AbstractThis paper presents a continuous time version of a stochastic investment model originally due to Wilkie. The model is constructed via stochastic differential equations. Explicit distributions are obtained in the case where the SDEs are driven by Brownian motion, which is the continuous time analogue of the time series with white noise residuals considered by Wilkie. In addition, the cases where the driving “noise” are stable processes and Gamma processes are considered.

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