Stock Price Trends
Stock price trends estimated using linear regression.
Summary
Key facts
- The primary trend is increasing.
- The growth rate of the primary trend is 75.48% per annum.
- KLAC price at the close of May 17, 2024 was $747.68 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 114.09% per annum.
- KLAC price at the close of May 17, 2024 was inside the secondary price channel.
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: February 21, 2023
End date: May 17, 2024
a = 3.7666
b = 0.0015
s = 0.0594
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 75.48%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0594) – 1
= 26.82%
February 21, 2023 calculations
Top border of price channel:
Exp(Y946)
= Exp(a + b × X946 + 2 × s)
= Exp(a + b × 1,373 + 2 × s)
= Exp(3.7666 + 0.0015 × 1,373 + 2 × 0.0594)
= Exp(6.0007)
= $403.72
Bottom border of price channel:
Exp(Y946)
= Exp(a + b × X946 – 2 × s)
= Exp(a + b × 1,373 – 2 × s)
= Exp(3.7666 + 0.0015 × 1,373 – 2 × 0.0594)
= Exp(5.7632)
= $318.35
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(3.7666 + 0.0015 × 1,824 + 2 × 0.0594)
= Exp(6.6956)
= $808.83
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(3.7666 + 0.0015 × 1,824 – 2 × 0.0594)
= Exp(6.4580)
= $637.80
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 75.48% per annum.
- KLAC price at the close of May 17, 2024 was $747.68 and was inside the primary price channel.
Secondary Trend
Start date: September 15, 2023
End date: May 17, 2024
a = 2.8232
b = 0.0021
s = 0.0473
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 114.09%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0473) – 1
= 20.85%
September 15, 2023 calculations
Top border of price channel:
Exp(Y1,089)
= Exp(a + b × X1,089 + 2 × s)
= Exp(a + b × 1,579 + 2 × s)
= Exp(2.8232 + 0.0021 × 1,579 + 2 × 0.0473)
= Exp(6.2110)
= $498.21
Bottom border of price channel:
Exp(Y1,089)
= Exp(a + b × X1,089 – 2 × s)
= Exp(a + b × 1,579 – 2 × s)
= Exp(2.8232 + 0.0021 × 1,579 – 2 × 0.0473)
= Exp(6.0217)
= $412.27
May 17, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,824 + 2 × s)
= Exp(2.8232 + 0.0021 × 1,824 + 2 × 0.0473)
= Exp(6.7220)
= $830.46
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.8232 + 0.0021 × 1,824 – 2 × 0.0473)
= Exp(6.5326)
= $687.21
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 114.09% per annum.
- KLAC price at the close of May 17, 2024 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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