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 73.17% per annum.
- KLAC price at the close of May 8, 2024 was $717.15 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 114.16% per annum.
- KLAC price at the close of May 8, 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 8, 2024
a = 3.8143
b = 0.0015
s = 0.0596
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 73.17%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0596) – 1
= 26.92%
February 21, 2023 calculations
Top border of price channel:
Exp(Y953)
= Exp(a + b × X953 + 2 × s)
= Exp(a + b × 1,384 + 2 × s)
= Exp(3.8143 + 0.0015 × 1,384 + 2 × 0.0596)
= Exp(6.0156)
= $409.77
Bottom border of price channel:
Exp(Y953)
= Exp(a + b × X953 – 2 × s)
= Exp(a + b × 1,384 – 2 × s)
= Exp(3.8143 + 0.0015 × 1,384 – 2 × 0.0596)
= Exp(5.7772)
= $322.87
May 8, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(3.8143 + 0.0015 × 1,826 + 2 × 0.0596)
= Exp(6.6806)
= $796.78
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(3.8143 + 0.0015 × 1,826 – 2 × 0.0596)
= Exp(6.4422)
= $627.79
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 73.17% per annum.
- KLAC price at the close of May 8, 2024 was $717.15 and was inside the primary price channel.
Secondary Trend
Start date: September 15, 2023
End date: May 8, 2024
a = 2.8040
b = 0.0021
s = 0.0474
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0021) – 1
= 114.16%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0474) – 1
= 20.90%
September 15, 2023 calculations
Top border of price channel:
Exp(Y1,096)
= Exp(a + b × X1,096 + 2 × s)
= Exp(a + b × 1,590 + 2 × s)
= Exp(2.8040 + 0.0021 × 1,590 + 2 × 0.0474)
= Exp(6.2163)
= $500.83
Bottom border of price channel:
Exp(Y1,096)
= Exp(a + b × X1,096 – 2 × s)
= Exp(a + b × 1,590 – 2 × s)
= Exp(2.8040 + 0.0021 × 1,590 – 2 × 0.0474)
= Exp(6.0265)
= $414.27
May 8, 2024 calculations
Top border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 + 2 × s)
= Exp(a + b × 1,826 + 2 × s)
= Exp(2.8040 + 0.0021 × 1,826 + 2 × 0.0474)
= Exp(6.7087)
= $819.47
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,826 – 2 × s)
= Exp(2.8040 + 0.0021 × 1,826 – 2 × 0.0474)
= Exp(6.5189)
= $677.83
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 114.16% per annum.
- KLAC price at the close of May 8, 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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