Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is decreasing.
- The decline rate of the primary trend is 33.08% per annum.
- KLAC price at the close of March 31, 2025 was $679.80 and was higher than the top border of the primary price channel by $16.08 (2.42%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 35.37% per annum.
- KLAC price at the close of March 31, 2025 was inside the secondary price channel.
- The direction of the secondary trend is opposite to the direction of the primary trend. This indicates a possible reversal in the direction of the primary trend.
Linear Regression Model
Model equation:
Yi = α + β × Xi + εi
Top border of price channel:
Exp(Yi) = Exp(a + b × Xi + 2 × s)
Bottom border of price channel:
Exp(Yi) = Exp(a + b × Xi – 2 × s)
where:
i - observation number
Yi - natural logarithm of KLAC price
Xi - time index, 1 day interval
σ - standard deviation of εi
a - estimator of α
b - estimator of β
s - estimator of σ
Exp() - calculates the exponent of e
Primary Trend
Start date: May 15, 2024
End date: January 13, 2025
a = 8.3843
b = -0.0011
s = 0.0608
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0011) – 1
= -33.08%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0608) – 1
= 27.55%
May 15, 2024 calculations
Top border of price channel:
Exp(Y1,037)
= Exp(a + b × X1,037 + 2 × s)
= Exp(a + b × 1,505 + 2 × s)
= Exp(8.3843 + -0.0011 × 1,505 + 2 × 0.0608)
= Exp(6.8500)
= $943.85
Bottom border of price channel:
Exp(Y1,037)
= Exp(a + b × X1,037 – 2 × s)
= Exp(a + b × 1,505 – 2 × s)
= Exp(8.3843 + -0.0011 × 1,505 – 2 × 0.0608)
= Exp(6.6066)
= $739.97
January 13, 2025 calculations
Top border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 + 2 × s)
= Exp(a + b × 1,748 + 2 × s)
= Exp(8.3843 + -0.0011 × 1,748 + 2 × 0.0608)
= Exp(6.5826)
= $722.40
Bottom border of price channel:
Exp(Y1,202)
= Exp(a + b × X1,202 – 2 × s)
= Exp(a + b × 1,748 – 2 × s)
= Exp(8.3843 + -0.0011 × 1,748 – 2 × 0.0608)
= Exp(6.3392)
= $566.36
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 33.08% per annum.
- KLAC price at the close of March 31, 2025 was $679.80 and was higher than the top border of the primary price channel by $16.08 (2.42%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: October 16, 2024
End date: March 27, 2025
a = 5.0878
b = 0.0008
s = 0.0494
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0008) – 1
= 35.37%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0494) – 1
= 21.84%
October 16, 2024 calculations
Top border of price channel:
Exp(Y1,143)
= Exp(a + b × X1,143 + 2 × s)
= Exp(a + b × 1,659 + 2 × s)
= Exp(5.0878 + 0.0008 × 1,659 + 2 × 0.0494)
= Exp(6.5628)
= $708.28
Bottom border of price channel:
Exp(Y1,143)
= Exp(a + b × X1,143 – 2 × s)
= Exp(a + b × 1,659 – 2 × s)
= Exp(5.0878 + 0.0008 × 1,659 – 2 × 0.0494)
= Exp(6.3653)
= $581.33
March 27, 2025 calculations
Top border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(5.0878 + 0.0008 × 1,821 + 2 × 0.0494)
= Exp(6.6972)
= $810.17
Bottom border of price channel:
Exp(Y1,253)
= Exp(a + b × X1,253 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(5.0878 + 0.0008 × 1,821 – 2 × 0.0494)
= Exp(6.4997)
= $664.95
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 35.37% per annum.
- KLAC price at the close of March 31, 2025 was inside the secondary price channel.
- Discover a new approach to trend analysis.
- Check the power of mathematical statistics.
- Price channels have never been so accurately estimated.
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