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 41.85% per annum.
- KLAC price at the close of January 17, 2025 was $757.47 and was higher than the top border of the primary price channel by $75.54 (11.08%). This indicates a possible reversal in the primary trend direction.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 59.94% per annum.
- KLAC price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $40.06 (5.58%).
- 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: June 10, 2024
End date: January 3, 2025
a = 9.1285
b = -0.0015
s = 0.0522
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × -0.0015) – 1
= -41.85%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0522) – 1
= 23.22%
June 10, 2024 calculations
Top border of price channel:
Exp(Y1,104)
= Exp(a + b × X1,104 + 2 × s)
= Exp(a + b × 1,602 + 2 × s)
= Exp(9.1285 + -0.0015 × 1,602 + 2 × 0.0522)
= Exp(6.8532)
= $946.92
Bottom border of price channel:
Exp(Y1,104)
= Exp(a + b × X1,104 – 2 × s)
= Exp(a + b × 1,602 – 2 × s)
= Exp(9.1285 + -0.0015 × 1,602 – 2 × 0.0522)
= Exp(6.6444)
= $768.45
January 3, 2025 calculations
Top border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 + 2 × s)
= Exp(a + b × 1,809 + 2 × s)
= Exp(9.1285 + -0.0015 × 1,809 + 2 × 0.0522)
= Exp(6.5457)
= $696.26
Bottom border of price channel:
Exp(Y1,247)
= Exp(a + b × X1,247 – 2 × s)
= Exp(a + b × 1,809 – 2 × s)
= Exp(9.1285 + -0.0015 × 1,809 – 2 × 0.0522)
= Exp(6.3369)
= $565.03
Description
- The primary trend is decreasing.
- The decline rate of the primary trend is 41.85% per annum.
- KLAC price at the close of January 17, 2025 was $757.47 and was higher than the top border of the primary price channel by $75.54 (11.08%). This indicates a possible reversal in the primary trend direction.
Secondary Trend
Start date: November 13, 2024
End date: January 15, 2025
a = 4.1756
b = 0.0013
s = 0.0273
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0013) – 1
= 59.94%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0273) – 1
= 11.55%
November 13, 2024 calculations
Top border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 + 2 × s)
= Exp(a + b × 1,758 + 2 × s)
= Exp(4.1756 + 0.0013 × 1,758 + 2 × 0.0273)
= Exp(6.4920)
= $659.86
Bottom border of price channel:
Exp(Y1,213)
= Exp(a + b × X1,213 – 2 × s)
= Exp(a + b × 1,758 – 2 × s)
= Exp(4.1756 + 0.0013 × 1,758 – 2 × 0.0273)
= Exp(6.3827)
= $591.53
January 15, 2025 calculations
Top border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 + 2 × s)
= Exp(a + b × 1,821 + 2 × s)
= Exp(4.1756 + 0.0013 × 1,821 + 2 × 0.0273)
= Exp(6.5731)
= $715.57
Bottom border of price channel:
Exp(Y1,254)
= Exp(a + b × X1,254 – 2 × s)
= Exp(a + b × 1,821 – 2 × s)
= Exp(4.1756 + 0.0013 × 1,821 – 2 × 0.0273)
= Exp(6.4638)
= $641.47
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 59.94% per annum.
- KLAC price at the close of January 17, 2025 was higher than the top border of the secondary price channel by $40.06 (5.58%).
- 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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