Akaike's FPE Research Articles

The discrimination of stenosed carotid bifurcation models with smooth and irregular plaque surface. Part II. The multivariate statistical analysis of ultrasonic Doppler velocity data

According to the conclusion of the first part of the paper the Doppler spectral indices were analyzed in a detailed manner to provide a means to differentiate bifurcation models with different irregularities. Autoregressive (AR) models using the Akaike FPE criterion were fitted to the curves of the spectral broadening index, turbulence intensity index and coefficient of symmetry. These curves were also submitted to the data reduction significant point extraction algorithm. The multivariate discriminant analysis was performed on parameter vectors containing coefficients of AR models, data reduction rate and data reduction error. The discriminant analysis allowed distinguishing models with the same degree of stenosis and different plaque surface characteristics on the basis of these vectors. The highest discrimination efficiency was observed for parameter vectors obtained from TBI and SKEW curves. The efficiency of discrimination was slightly higher for more severely stenosed models.

An Improvement of Akaike's FPE Criterion to Reduce its Variability

The selection of the number of past observations to be included in a linear predictor (the order of the predictor) should be done with minimum variability, since it is not taken into account in the inference stage. For finite time series, there is a trade‐off between variability and optimality (in the sense of mean squared prediction error). The widely used Akaike criteria, FPE and AIC, lead to highly variable estimated orders, whereas consistent criteria are downward biased when the optimal order increases with the sample size. In this paper we propose the use of a sequence of tests to analyse the order selected with FPE. The result is a new identification criterion. In a simulation study, this criterion is shown to reach a compromise with respect to the above‐mentioned trade‐off. Some asymptotic properties are also derived.

Domestic and International Sources of Inflation in Developing Countries: Some Evidence from the Monetary Approach

Using the monetary approach, this paper examines empirically the causes of inflation in twenty-five developing countries. In addition to money supply, the underlying money demand function and foreign exchange rates are taken into account in the inflationary process. The lag structures are determined by Akaike's FPE criterion and the exogeneity assumptions are assessed by Granger-type causality tests. The results suggest that the monetary approach provides adequate explanation of inflation across all countries examined. Besides changes in expected inflation and foreign exchange rates, movements in base money in these countries have significantly contributed to their inflationary pressures. [134, 431]

Asymptotical optimality of Akaike's final prediction error

Akaike's FPE procedure as a data dependent method of selecting the degree and the number of pieces of a piece wise polynomial estimator of a regression function is proposed here. The proposed method requires no assumption of smoothness of the regression function. It is shown the asymptotic efficiency of FPE is achieved both in a.s. convergence and in theg-th mean convergence.

Selecting the order of autoregressive models from small samples

The weak parameter criterion WPC is introduced as a means for model order selection. It is based on the same principles as Mallows' C p and the FPE and AIC criteria of Akaike. According to the WPC, parameters are weak and should be removed if the squares of their estimates are less than twice the expectation for a white noise signal. Roughly speaking, the square of an estimate must exceed twice its variance. Due to the conceptual simplicity, this criterion remains useful for small samples where the asymptotical properties are no longer valid. If the maximum order considered is \sqrt{N} or less, the difference between Akaike's FPE and AIC criteria on one hand and the WPC on the other hand remains small and the use of AIC or FPE may be justified. However, it is advised to use the WPC for higher maximum orders. By using different variances in the WPC for Yule-Walker and for Burg estimates, it is achieved that the average selected WPC order in small samples depends mainly on the given data and no longer on the method of parameter estimation.

An Optimal Selection of Regression Variables

An asymptotically optimal selection of regression variables is proposed. The key assumption is that the number of control variables is infinite or increases with the sample size. It is also shown that Mallows's Cp', Akaike's FPE and aic methods are all asymptotically equivalent to this method.

An optimal selection of regression variables

SUMMARY An asymptotically optimal selection of regression variables is proposed. The key assumption is that the number of control variables is infinite or increases with the sample size. It is also shown that Mallows's Qp, Akaike's FPE -and AIC methods are all asymptotically equivalent to this method.

Some properties of the order of an autoregressive model selected by a generalization of Akaike∘s EPF criterion

SUMMARY The asymptotic distribution of the order of an autoregression selected by a generalization of Akaike's FPE criterion is given. Some of the properties of the distribution are investigated. The use of this criterion is illustrated by a simulation study.

Statistical Identification of Ship's Course Keeping Motion and Optimal Control

In this paper, the ship's course keeping motion is represented by an Auto Regressive model (A. R. model) in the time series analysis and it is shown that the Akaike's FPE method is effective to the determination of the order of the model. This method is immediately applied to the estimation of spectra of some ship's motions and we designed one optimal controller using the Dynamic Programming.According to our digital simulation, our controller shows some remarkable characteristics and in particular, through a smoother and a lower rudder motion than the manual or the present auto-pilot steering, ship's motions (especially Yawing and Rolling) are considerably reduced. This last point is expected to contribute to the development of the Direct Digital Control.