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 75.88% per annum.
- LRCX price at the close of April 26, 2024 was $925.37 and was inside the primary price channel.
- The secondary trend is increasing.
- The growth rate of the secondary trend is 144.10% per annum.
- LRCX price at the close of April 26, 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 LRCX 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: September 15, 2022
End date: April 26, 2024
a = 4.0314
b = 0.0015
s = 0.0744
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0015) – 1
= 75.88%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0744) – 1
= 34.67%
September 15, 2022 calculations
Top border of price channel:
Exp(Y853)
= Exp(a + b × X853 + 2 × s)
= Exp(a + b × 1,235 + 2 × s)
= Exp(4.0314 + 0.0015 × 1,235 + 2 × 0.0744)
= Exp(6.0907)
= $441.73
Bottom border of price channel:
Exp(Y853)
= Exp(a + b × X853 – 2 × s)
= Exp(a + b × 1,235 – 2 × s)
= Exp(4.0314 + 0.0015 × 1,235 – 2 × 0.0744)
= Exp(5.7930)
= $328.00
April 26, 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(4.0314 + 0.0015 × 1,824 + 2 × 0.0744)
= Exp(7.0019)
= $1,098.68
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(4.0314 + 0.0015 × 1,824 – 2 × 0.0744)
= Exp(6.7042)
= $815.82
Description
- The primary trend is increasing.
- The growth rate of the primary trend is 75.88% per annum.
- LRCX price at the close of April 26, 2024 was $925.37 and was inside the primary price channel.
Secondary Trend
Start date: September 19, 2023
End date: April 26, 2024
a = 2.4685
b = 0.0024
s = 0.0522
Annual growth rate:
Exp(365 × b) – 1
= Exp(365 × 0.0024) – 1
= 144.10%
Price channel spread:
Exp(4 × s) – 1
= Exp(4 × 0.0522) – 1
= 23.20%
September 19, 2023 calculations
Top border of price channel:
Exp(Y1,106)
= Exp(a + b × X1,106 + 2 × s)
= Exp(a + b × 1,604 + 2 × s)
= Exp(2.4685 + 0.0024 × 1,604 + 2 × 0.0522)
= Exp(6.4945)
= $661.49
Bottom border of price channel:
Exp(Y1,106)
= Exp(a + b × X1,106 – 2 × s)
= Exp(a + b × 1,604 – 2 × s)
= Exp(2.4685 + 0.0024 × 1,604 – 2 × 0.0522)
= Exp(6.2859)
= $536.93
April 26, 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(2.4685 + 0.0024 × 1,824 + 2 × 0.0522)
= Exp(7.0324)
= $1,132.73
Bottom border of price channel:
Exp(Y1,258)
= Exp(a + b × X1,258 – 2 × s)
= Exp(a + b × 1,824 – 2 × s)
= Exp(2.4685 + 0.0024 × 1,824 – 2 × 0.0522)
= Exp(6.8237)
= $919.43
Description
- The secondary trend is increasing.
- The growth rate of the secondary trend is 144.10% per annum.
- LRCX price at the close of April 26, 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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