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 February 20, 2025 was $777.63 and was higher than the top border of the primary price channel by $83.22 (11.98%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 141.39% per annum.
- KLAC price at the close of February 20, 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 = 8.4306
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(Y1,065)
= Exp(a + b × X1,065 + 2 × s)
= Exp(a + b × 1,545 + 2 × s)
= Exp(8.4306 + -0.0011 × 1,545 + 2 × 0.0608)
= Exp(6.8523)
= $946.03
Bottom border of price channel:
Exp(Y1,065)
= Exp(a + b × X1,065 – 2 × s)
= Exp(a + b × 1,545 – 2 × s)
= Exp(8.4306 + -0.0011 × 1,545 – 2 × 0.0608)
= Exp(6.6089)
= $741.68
January 13, 2025 calculations
Top border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 + 2 × s)
= Exp(a + b × 1,788 + 2 × s)
= Exp(8.4306 + -0.0011 × 1,788 + 2 × 0.0608)
= Exp(6.5849)
= $724.07
Bottom border of price channel:
Exp(Y1,230)
= Exp(a + b × X1,230 – 2 × s)
= Exp(a + b × 1,788 – 2 × s)
= Exp(8.4306 + -0.0011 × 1,788 – 2 × 0.0608)
= Exp(6.3415)
= $567.67
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 33.08% per annum.
- KLAC price at the close of February 20, 2025 was $777.63 and was higher than the top border of the primary price channel by $83.22 (11.98%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 15, 2024
End date: February 20, 2025
a = 2.2384
b = 0.0024
s = 0.0335
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0024) – 1
= 141.39%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0335) – 1
= 14.32%
November 15, 2024 calculations
Top border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 + 2 × s)
= Exp(a + b × 1,729 + 2 × s)
= Exp(2.2384 + 0.0024 × 1,729 + 2 × 0.0335)
= Exp(6.4798)
= $651.86
Bottom border of price channel:
Exp(Y1,193)
= Exp(a + b × X1,193 – 2 × s)
= Exp(a + b × 1,729 – 2 × s)
= Exp(2.2384 + 0.0024 × 1,729 – 2 × 0.0335)
= Exp(6.3460)
= $570.19
February 20, 2025 calculations
Top border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.2384 + 0.0024 × 1,826 + 2 × 0.0335)
= Exp(6.7140)
= $823.88
Bottom border of price channel:
Exp(Y1,256)
= Exp(a + b × X1,256 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.2384 + 0.0024 × 1,826 – 2 × 0.0335)
= Exp(6.5802)
= $720.65
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 141.39% per annum.
- KLAC price at the close of February 20, 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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