• Journal of The Korean Astronomical Society
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• v.50 no.2
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• pp.21-27
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• 2017

The autoregressive method provides a univariate procedure to predict the future sunspot number (SSN) based on past record. The strength of this method lies in the possibility that from past data it yields the SSN in the future as a function of time. On the other hand, its major limitation comes from the intrinsic complexity of solar magnetic activity that may deviate from the linear stationary process assumption that is the basis of the autoregressive model. By analyzing the residual errors produced by the method, we have obtained the following conclusions: (1) the optimal duration of the past time for the forecast is found to be 8.5 years; (2) the standard error increases with prediction horizon and the errors are mostly systematic ones resulting from the incompleteness of the autoregressive model; (3) there is a tendency that the predicted value is underestimated in the activity rising phase, while it is overestimated in the declining phase; (5) the model prediction of a new Solar Cycle is fairly good when it is similar to the previous one, but is bad when the new cycle is much different from the previous one; (6) a reasonably good prediction of a new cycle can be made using the AR model 1.5 years after the start of the cycle. In addition, we predict the next cycle (Solar Cycle 25) will reach the peak in 2024 at the activity level similar to the current cycle.

• Publications of The Korean Astronomical Society
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• v.14 no.2
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• pp.91-102
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• 1999

We have made intensive calculations on the maximum relative sunspot number and the date of solar maximum of 23rd solar cycle, by using the statistical and precursor methods to predict solar activity cycle. According to our results of solar data processing by statistical method, solar maximum comes at between February and July of 2000 year and at that time, the smoothed sunspot number will reach to $114.3\~122.8$. while precursor method gives rather dispersed value of $118\~17$ maximum sunspot number. It is found that prediction by statistical method using smoothed relative sunspot number is more accurate than by any method to use any data of 10.7cm radio fluxes and geomagnetic aa, Ap indexes, from the full analysis of solar cycle pattern of these data. In fact, current ascending pattern of 23rd solar cycle supports positively our predicted values. Predicted results by precursor method for $Ap_{avg},\;aa_{31-36}$ indexes show similar values to those by statistical method. Therefore, these indexes can be used as new precursors for the prediction of 23rd or next solar cycle.

• The Bulletin of The Korean Astronomical Society
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• v.41 no.1
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• pp.45.3-46
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• 2016

Solar activity shows a self-similarity as it has many periods of activity cycle in the time series of long-term observation, such as 13.5, 51, 150, 300 days, and 11, 88 years and so on. Since fractal dimension is a quantitative parameter for this kind of an irregular time series, we applied this method to long-term observations including sunspot number, total solar irradiance, and 3.75 GHz solar radio flux to predict the start and maximum times as well as expected maximum sunspot number for the next solar cycle. As a result, we found that the radio flux data tend to have lower fractal dimensions than the sunspot number data, which means that the radio emission from the sun is more regular than the solar activity expressed by sunspot number. Based on the relation between radio flux of 3.75 GHz and sunspot number, we could calculate the expected maximum sunspot number of solar cycle 24 as 156, while the observed value is 146. For the maximum time, estimated mean values from 7 different observations are January 2013 and this is quite different to observed value of February 2014. We speculate this is from extraordinary extended properties of solar cycle 24. As the cycle length of solar cycle 24, 10.1 to 12.8 years are expected, and the mean value is 11.0. This implies that the next solar cycle will be started at December 2019.

• Publications of The Korean Astronomical Society
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• v.14 no.2
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• pp.103-112
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• 1999

We have investigated the solar activity variation with period shorter than 1000 days, through Fourier transformation of solar cycle 21 and 22 data. And real time predictions of the flare maximum intensity have been made by multilinear regression method to allow the use of multivariate vectors of sunspot groups or active region characteristics. In addition, we have examined the evolution of magnetic field and current density in active regions at times before and after flare occurrence, to check short term variability of solar activity. According to our results of calculation, solar activity changes with periods of 27.1, 28.0, 52.1, 156.3, 333.3 days for solar cycle 21 and of 26.5, 27.1, 28.9, 54.1, 154, 176.7, 384.6 days for solar cycle 22. Periodic components of about 27, 28, 53, 155 days are found simultaneously at all of two solar cycles. Finally, from our intensive analysis of solar activity data for three different terms of $1977\~1982,\; 1975\~1998,\;and\;1978\~1982$, we find out that our predictions coincide with observations at hit rate of $76\%,\;63\%$, 59 respectively.

• Journal of Astronomy and Space Sciences
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• v.23 no.3
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• pp.227-236
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• 2006

The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center) and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89) between the observed and predicted maximum sunspot numbers in the solar cycles.

• Journal of Astronomy and Space Sciences
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• v.31 no.2
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• pp.149-157
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• 2014

As the prediction of geomagnetic storms is becoming an important and practical problem, conditions in the Earth's magnetosphere have been studied rigorously in terms of those in the interplanetary space. Another approach to space weather forecast is to deal with it as a probabilistic geomagnetic storm forecasting problem. In this study, we carry out detailed statistical analysis of solar wind parameters and geomagnetic indices examining the dependence of the distribution on the solar cycle and annual variations. Our main findings are as follows: (1) The distribution of parameters obtained via the superimposed epoch method follows the Gaussian distribution. (2) When solar activity is at its maximum the mean value of the distribution is shifted to the direction indicating the intense environment. Furthermore, the width of the distribution becomes wider at its maximum than at its minimum so that more extreme case can be expected. (3) The distribution of some certain heliospheric parameters is less sensitive to the phase of the solar cycle and annual variations. (4) The distribution of the eastward component of the interplanetary electric field BV and the solar wind driving function BV2, however, appears to be all dependent on the solar maximum/minimum, the descending/ascending phases of the solar cycle and the equinoxes/solstices. (5) The distribution of the AE index and the Dst index shares statistical features closely with BV and $BV^2$ compared with other heliospheric parameters. In this sense, BV and $BV^2$ are more robust proxies of the geomagnetic storm. We conclude by pointing out that our results allow us to step forward in providing the occurrence probability of geomagnetic storms for space weather and physical modeling.

• Journal of The Korean Astronomical Society
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• v.40 no.4
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• pp.99-106
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• 2007

Statistical analyses were performed to investigate the relative success and accuracy of daily maximum X-ray flux (MXF) predictions, using both multilinear regression and autoregressive time-series prediction methods. As input data for this work, we used 14 solar activity parameters recorded over the prior 2 year period (1989-1990) during the solar maximum of cycle 22. We applied the multilinear regression method to the following three groups: all 14 variables (G1), the 2 so-called 'cause' variables (sunspot complexity and sunspot group area) showing the highest correlations with MXF (G2), and the 2 'effect' variables (previous day MXF and the number of flares stronger than C4 class) showing the highest correlations with MXF (G3). For the advanced three days forecast, we applied the autoregressive timeseries method to the MXF data (GT). We compared the statistical results of these groups for 1991 data, using several statistical measures obtained from a $2{\times}2$ contingency table for forecasted versus observed events. As a result, we found that the statistical results of G1 and G3 are nearly the same each other and the 'effect' variables (G3) are more reliable predictors than the 'cause' variables. It is also found that while the statistical results of GT are a little worse than those of G1 for relatively weak flares, they are comparable to each other for strong flares. In general, all statistical measures show good predictions from all groups, provided that the flares are weaker than about M5 class; stronger flares rapidly become difficult to predict well, which is probably due to statistical inaccuracies arising from their rarity. Our statistical results of all flares except for the X-class flares were confirmed by Yates' $X^2$ statistical significance tests, at the 99% confidence level. Based on our model testing, we recommend a practical strategy for solar X-ray flare predictions.

• The Bulletin of The Korean Astronomical Society
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• v.36 no.2
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• pp.100.1-100.1
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• 2011

Everybody wants to see the future, but nobody does for sure. Reliably forecasting the solar activity in the near future looks like an easy task, but in fact still remains one of difficult problems in the solar-terrestrial research. We have sought for good univariate methods that can predict future smoothed sunspot numbers reasonably well based on past smoothed sunspot number data only. Here we consider a specific method we call principal component-and-autoregression (PCAR) method. The variation of sunspot number during a period of finite duration (past) before an epoch (present) is modeled by a linear combination of a small number of dominant principal components, and this model is extended to the period (future) beyond the epoch using the autoregressive model of finite order. From the application of this method, we find that the $24^{th}$ solar maximum is likely to occur near the end of the year 2013 (and there is a possibility that it occurs earlier near the start of 2013), and to have a peak sunspot number of about 86, indicating that the activity of the $24^{th}$ cycle will be weaker than the average. We will discuss how much this estimate is reliable.